Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

Dear sir in this problem should accept five boundaryconditions but it is not working for five boundary conditions and showing the following error please can you tell why it is like this ??

Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 4, got 5
Error, (in plots:-display) expecting plot structures but received: [fplt[1], fplt[2], fplt[3], fplt[4], fplt[5], fplt[6], fplt[7]]
Error, (in plots:-display) expecting plot structures but received: [tplt[1], tplt[2], tplt[3], tplt[4], tplt[5], tplt[6], tplt[7]]
 

and for the progam please check the following link

stretching_cylinder_new1.mw

Hi MaplePrimes,

This YouTube video has a nice puzzle. 

It is titled "Can you solve the locker riddle". 
My first blush was to consider modular arithmatic
https://www.youtube.com/watch?v=c18GjbnZXMw

Here is a maple page -
divisors_excercise.mw

divisors_excercise.pdf

Have a very fine rest of the day.

Regards,
Matt

 

I assigned

before an algebraic calculation so I would like to get  or have the program print the 70 digits of the answer and not just 10 digits. Because when I press ENTER, I get only 10 digits.

 

Hi Maple Primes,

Can this code be improved?

I know that the Goldbach Conjecture has been checked with computer tools above 10^10.

Request for comments.

check_g_conjecture_26_b.mw

check_g_conjecture_26_b.pdf

Regards

Matt

 

staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw
 

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(A) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A[j]*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(20) = 1, theta(0) = 1+s*(D(theta))(0), theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do:

 

 

``

l := 1:

1

 

[0, 1, 1.5]

 

.5

 

[blue, green, red, yellow]

(2)

for j to nops(n1) do R4 := 2*n1[j]/(n1[j]+1); R5 := 2*p1/(n1[j]+1); R6 := 2/(n1[j]+1); sol2 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R4*(1-(diff(f(eta), eta))^2)-M1*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr1*f(eta)*(diff(theta(eta), eta))-R5*pr1*(diff(f(eta), eta))*theta(eta)+R6*(A1*(diff(f(eta), eta))+B1*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L1+b1*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s1*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol2, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol2, sol1, [[eta, diff(f(eta), eta)], [eta, diff(f(eta), eta)]], color = K1[j], axes = boxed); tplt[j] := plots[odeplot](sol2, [[eta, theta(eta)]], color = K1[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n1))]); plots:-display([seq(tplt[j], j = 1 .. nops(n1))])

Error, (in plots/odeplot) invalid argument: sol1

 

 

 

``

``

sol1(0);

[eta = 0., f(eta) = 1.00000000000000044, diff(f(eta), eta) = .899599635987511914, diff(diff(f(eta), eta), eta) = -.200800728024976643, theta(eta) = 1.18657688243172332, diff(theta(eta), eta) = .373153764863445037]

(3)

sol1(.1)

[eta = .1, f(eta) = 1.08902313464617162, diff(f(eta), eta) = .881503890693141945, diff(diff(f(eta), eta), eta) = -.162309073227910134, theta(eta) = 1.22040489003745489, diff(theta(eta), eta) = .304232440930656767]

(4)

sol1(.2)

[eta = .2, f(eta) = 1.17641763749368966, diff(f(eta), eta) = .866916683092940898, diff(diff(f(eta), eta), eta) = -.130454301210374102, theta(eta) = 1.24759607023709362, diff(theta(eta), eta) = .240488988787701030]

(5)

sol1(.3)

[eta = .3, f(eta) = 1.19045803452309284, diff(f(eta), eta) = .579367537136023514, diff(diff(f(eta), eta), eta) = -.285675511621370782, theta(eta) = 1.18389221591022696, diff(theta(eta), eta) = .146013974567769960]

(6)

sol1(.4)

[eta = .4, f(eta) = 1.40000000000000034, diff(f(eta), eta) = 1.00000000000000022, diff(diff(f(eta), eta), eta) = -0.243774513041384287e-17, theta(eta) = .625958972186505536, diff(theta(eta), eta) = -.314549395236395634]

(7)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(8)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(9)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(10)

``

``

``

 

``

``

NULL


 

Download staganation_point11.mw

 

in this program im trying to combine the result, but it showing some error can help me please

 

 

 

Hi everybody,

So today is 10-28-2016 and I explored Leyland Numbers for the first time, on Maple.  Please see my example file and let me know what your impression is.

x_to_the_yth_power_and_y_to_the_xth_power_take_4.mw

x_to_the_yth_power_and_y_to_the_xth_power_take_4.pdf

I have included a .pdf file so that the caual internet observer can also be aware of this information.

Regards,
Matt

 

> restart;

with(plots);

pr := .72; p := 0; n := [.5, 1, 1.5]; s := 0; a := .2; b := 0; L := [red, blue, green]; l := 0; k := 1;

for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n);

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2) = 0, diff(diff(theta(eta), eta), eta)+pr*k*f(eta)*(diff(theta(eta), eta))+R2*pr*k*(diff(f(eta), eta))*theta(eta)+(2*(a*(diff(f(eta), eta))+b*theta(eta)))/(1+n[j]) = 0, f(0) = 1, (D(f))(0) = b*((D@@2)(f))(0), (D(f))(1.8) = 0, theta(0) = 1+s*(D(theta))(0), theta(1.8) = 1], numeric, method = bvp);

fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = L[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(tplt[j], j = 1 .. nops(n))]);

 

staganation_point1.mw
 

can we chage the axis sir ?? like  f'' vs eta to f'' vs lambda.

``

restart

l := 1:

1

 

1.5

 

.5

 

[blue, green, red, yellow]

(1)

``

for j to nops(p) do R1 := 2*n/(n+1); R2 := 2*p[j]/(n+1); R3 := 2/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal); fplt[j] := plots[odeplot](sol1, [eta, diff(f(eta), eta)], color = K[j], axes = boxed) end do:

 

 

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

 

sol1(0)

sol1(0)

(2)

sol1(.1)

[eta = .1, f(eta) = 1.05958091104306206, diff(f(eta), eta) = .643210624614908300, diff(diff(f(eta), eta), eta) = .881482678165403044, theta(eta) = .623284688471349546, diff(theta(eta), eta) = -.578039450700496560]

(3)

sol1(.2)

[eta = .2, f(eta) = 1.12800452943200891, diff(f(eta), eta) = .722346769554029544, diff(diff(f(eta), eta), eta) = .706526135439307756, theta(eta) = .568123251856343492, diff(theta(eta), eta) = -.525530979400813946]

(4)

sol1(.3)

[eta = .3, f(eta) = 1.20351830506746449, diff(f(eta), eta) = .785511903074783246, diff(diff(f(eta), eta), eta) = .561442941644520022, theta(eta) = .518103974464032668, diff(theta(eta), eta) = -.475257424178228970]

(5)

sol1(.4)

[eta = .4, f(eta) = 1.28466826824405134, diff(f(eta), eta) = .835505660630676662, diff(diff(f(eta), eta), eta) = .442470716586289281, theta(eta) = .472985640642506311, diff(theta(eta), eta) = -.427567049032814172]

(6)

sol1(.5)

[eta = .5, f(eta) = 1.37026161183094430, diff(f(eta), eta) = .874752886901313142, diff(diff(f(eta), eta), eta) = .345911467377074400, theta(eta) = .432494259338694842, diff(theta(eta), eta) = -.382764248064397461]

(7)

sol1(.6)

[eta = .6, f(eta) = 1.36678221814533528, diff(f(eta), eta) = .771028661281065508, diff(diff(f(eta), eta), eta) = .407805382194403932, theta(eta) = .876413930517023876, diff(theta(eta), eta) = -.197648778495384870]

(8)

sol1(2)

[eta = 2., f(eta) = 2.66120522956795602, diff(f(eta), eta) = .991532161353848585, diff(diff(f(eta), eta), eta) = 0.251405465681268682e-1, theta(eta) = .635967939441598018, diff(theta(eta), eta) = -.144641270049362308]

(9)

``

``

``

 

``


 

Download staganation_point1.mw

 

 

 

 

 

http://www.sciencedirect.com/science/article/pii/S100757041300508X> restart;
> l := 1; p := 1; A := .5; B := .5; pr := 1; n := [.5, 1, 1.5]; M := 0; b := .5; L := 0; s := .5; K := [blue, green];
                                      1
                                [0.5, 1, 1.5]
                                [blue, green]

> for j to nops(n) do R1 := 2*n[j]/(n[j]+1); R2 := 2*p/(n[j]+1); R3 := 2/(n[j]+1);

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp);

plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red);

fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = K[j], axes = boxed); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed);

tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do;

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

plots:-display([seq(tplt[j], j = 1 .. nops(n))]);
http://www.sciencedirect.com/science/article/pii/S100757041300508X

Dear sir 

I am trying to plot the following link paper graphs for practice but I getting the plots for only one set of values here in this paper they plotted many so if you dont muned can help in this case. For example in this first graph named as Fig.1. please can you do this favour... and the paper link is  http://www.sciencedirect.com/science/article/pii/S100757041300508X

 

Hi Mapleprimes,

I have made this little procedure with Maple. 

check_g_conjecture_10.pdf

similar to this next one check_g_conjecture_10.mw

This may be worth a look.

Regards,

Matthew

P.S.   see  https://en.wikipedia.org/wiki/Goldbach%27s_conjecture

In My Humble Opinion, Wikipedia is a good crowd sourced resource.

 

> restart; for j to nops(n) do sys := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))+1-(diff(f(eta), eta))^2 = 0, (diff(diff(theta(eta), eta), eta))/pr+f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta) = 0; bcs := f(0) = 0, (D(f))(0) = l+b*((D@@2)(f))(0), (D(f))(-.5) = 1, theta(0) = 1+s*(D(theta))(-.5), theta(2) = 0; n := [1, 2, 3, 4, 5, 6]; pr := .71; p := 0; q := 0; b := 0; l := 0; s := 0; L := [red, blue, orange]; R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n); p := proc (f1, th1, { output::name := 'number' }) local res1, fvals, thvals, res2; option remember; res1 := dsolve({sys, f(1) = 0, theta(0) = 1+th1, (D(f))(0) = f1, (D(theta))(0) = th1, ((D@@2)(f))(0) = f1-1}, numeric, :-output = listprocedure); fvals := (subs(res1, [seq(diff(f(eta), [`$`(eta, i)]), i = 0 .. 2)]))(0); thvals := (subs(res1, [seq(diff(theta(eta), [`$`(eta, i)]), i = 0 .. 1)]))(0); res2 := dsolve({sys, f(0) = fvals[1], theta(0) = thvals[1], theta(5) = 0, (D(f))(0) = fvals[2], (D(f))(5) = 1}, numeric, :-output = listprocedure); if output = 'number' then [fvals[3]-(subs(res2, diff(f(eta), `$`(eta, 2))))(0), thvals[2]-(subs(res2, diff(theta(eta), eta)))(0)] else res1, res2 end if end proc; p1 := proc (f1, th1) p(args)[1] end proc; p2 := proc (f1, th1) p(args)[2] end proc; p(.3, -.2); par := fsolve([p1, p2], [.3, -.2]); res1, res2 := p(op(par), output = xxx); plots:-display(plots:-odeplot(res1, [[eta, f(eta)], [eta, theta(eta)]]), plots:-odeplot(res2, [[eta, f(eta)], [eta, theta(eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta, eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta, eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta)]])); fplt[j] := plots[odeplot](res1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](res1, [[eta, theta(eta)]], color = L[j], axes = boxed) end do;
> plots:-display([seq(fplt[j], j = 1 .. nops(n))]);


Dear Sir

In my above problem i trying to plot for set of values of n but in plot command it not executing , can you do this why it is not executing ??

 

> restart;
> n := [1, 2, 3, 4, 5]; pr := .71; p := 0; q := 0; b := 0; l := 0; s := 0;
> for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n); sys := diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+1-(diff(f(eta), eta))^2 = 0, (diff(diff(theta(eta), eta), eta))/pr+f(eta)*(diff(theta(eta), eta))-R2*(diff(f(eta), eta))*theta(eta) = 0; bcs := f(0) = 0, (D(f))(0) = l+b*((D@@2)(f))(0), (D(f))(-.5) = 1, theta(0) = 1+s*(D(theta))(0), theta(-.5) = 0; proc (f1, th1, { output::name := 'number' }) local res1, fvals, thvals, res2; option remember; res1 := dsolve({sys, f(0) = 0, theta(0) = 1+th1, (D(f))(-2) = f1, (D(theta))(-2) = th1, ((D@@2)(f))(0) = f1-1}, numeric, :-output = listprocedure); fvals := (subs(res1, [seq(diff(f(eta), [`$`(eta, i)]), i = 0 .. 2)]))(0); thvals := (subs(res1, [seq(diff(theta(eta), [`$`(eta, i)]), i = 0 .. 1)]))(0); res2 := dsolve({sys, f(0) = fvals[1], theta(0) = thvals[1], theta(1) = 0, (D(f))(0) = fvals[2], (D(f))(1) = 0}, numeric, :-output = listprocedure); if output = 'number' then [fvals[3]-(subs(res2, diff(f(eta), `$`(eta, 2))))(0), thvals[2]-(subs(res2, diff(theta(eta), eta)))(0)] else res1, res2 end if end proc; p1 := proc (f1, th1) p(args)[1] end proc; p2 := proc (f1, th1) p(args)[2] end proc; p(.3, -.2); par := fsolve([p1, p2], [.3, -.2]); res1, res2 := p(op(par), output = xxx); plots:-display(plots:-odeplot(res1, [[eta, f(eta)], [eta, theta(eta)]]), plots:-odeplot(res2, [[eta, f(eta)], [eta, theta(eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta, eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta, eta)]])); fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = L[j], axes = boxed) end do;


Dear Sir

In this above problem it showing that error as  Error, cannot split rhs for multiple assignment please can you tell why it is showing like this  ?? and where i did multiple assignments ??

Dear sir

 

In my ode problem i do not know that how to set range (eta) from -2 to 2 please can  you help me.

> restart;
> with(plots);
> n := [0, .5, 1, 5]; pr := .71; p := 0; l := [1, 2, 3]; b := 0; s := 0; L := [green, blue, black, gold];
                         [green, blue, black, gold]
> R1 := 2*n/(n+1);
                              2 [0, 0.5, 1, 5]
                             ------------------
                             [0, 0.5, 1, 5] + 1
for j from 1 to nops(l) do; for j from 1 to nops(n) do        R1 := 2*n[j]/(1+n[j]);        R2 := 2*p/(1+n[j]); sol1 := dsolve([diff(diff(diff(f(eta),eta),eta),eta)+f(eta)*diff(diff(f(eta),eta),eta)+R1*(1-diff(f(eta),eta)^2) = 0, (1/pr)*diff(diff(theta(eta),eta),eta)+f(eta)*diff(theta(eta),eta)-R2*diff(f(eta),eta)*theta(eta) = 0, f(0) = 0, (D(f))(0) = l+b*((D@@2)(f))(0), (D(f))(-2) =1, theta(0) = 1+s*(D(theta))(0), theta(-2) = 0], numeric, method = bvp); fplt[j]:= plots[odeplot](sol1,[eta,diff(diff(f(eta),eta),eta)],color=["blue","black","orange"]);         tplt[j]:= plots[odeplot](sol1, [eta,theta(eta)],color=L[j]); fplt[j]:= plots[odeplot](sol1,[eta,diff(f(eta),eta)],color=L[j]);      od:od:

 


Error, (in dsolve/numeric/bvp) unable to store 'Limit([eta, 2*eta, 3*eta]+eta^2*[.250000000000000, .500000000000000, .750000000000000]-.250000000000000*eta^2, eta = -2., left)' when datatype=float[8]
> plots:-display([seq(fplt[j], j = 1 .. nops(n))], color = [green, red], [seq(fplt[j], j = 1 .. nops(l))]);

> sol1(0);

Dear sir

In the  above problem i tried to write a nested program but its not executing and showing the error as Error, (in dsolve/numeric/bvp) unable to store 'Limit([eta, 2*eta, 3*eta]+eta^2*, i want the plot range from -2 to 2 but taking only 0 to -2 ,and -2.5 to 3 but taking only 0 to 1

> restart;
> with(plots);
> pr := .72; p := 0; n := [2, 3, 4, 5]; s := 1; a := .2; b := 1;
> R1 := 2*n/(n+1);
                               2 [2, 3, 4, 5]
                              ----------------
                              [2, 3, 4, 5] + 1
> R2 := 2*p/(n+1);
                                      0
>
>
> for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n[j]); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2) = 0, diff(diff(theta(eta), eta), eta)+pr*s^f(eta)*(diff(theta(eta), eta))+R2*pr*s*(diff(f(eta), eta))*theta(eta)+2*(a*(diff(f(eta), eta))+b*theta(eta))/(n[j]-1) = 0, f(0) = 0, (D(f))(0) = 1+b*((D@@2)(f))(0), (D(f))(5) = 0, theta(0) = 1+s*(D(theta))(0), theta(5) = 0], numeric, method = bvp); fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], axes = boxed) end do;
>
> plots:-display([seq(fplt[j], j = 1 .. nops(n))]);

 

> plots:-display([seq(tplt[j], j = 1 .. nops(n))]);

 

 

Dear sir

In the above problem graph, i am getting all the lines are in same color then how to identify the lines of different values like n=2,3,4,5,6(or can we set different color for different values of n for each line)

> restart;
> with(plots);
> pr := .72; p := 0; n := 1; s := 1; a := [-0.5,0.0,0.5]; b := 1;
> R1 := 2*n/(n+1);
                                      1
> R2 := 2*p/(n+1);
                                      0
>
>
> for j to nops(a) do R1 := 2*n/(n+1); R2 := 2*p/(n+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2) = 0, diff(diff(theta(eta), eta), eta)+pr*s^f(eta)*(diff(theta(eta), eta))+R2*pr*s*(diff(f(eta), eta))*theta(eta)+2*(a[j]*(diff(f(eta), eta))+b*theta(eta))/(n+1) = 0, f(-.5) = 0, (D(f))(0) = 1+b*((D@@2)(f))(0), (D(f))(5) = 0, theta(-.5) = 1+s*(D(theta))(0), theta(5) = 0], numeric, method = bvp); fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = ["blue", "black", "orange"]); tplt[j] := plots[odeplot](sol1, [eta, theta(eta)], color = setcolors(["red", "Coral"])) end do;
Error, (in dsolve/numeric/process_input) boundary conditions specified at too many points: {0, 5, -1/2}, can only solve two-point boundary value problems
>
> plots:-display([seq(fplt[j], j = 1 .. nops(a))], color = [green, red]);

> plots:-display([seq(tplt[j], j = 1 .. nops(a))], color = [green, red]);

 

Dear sir,

In this program i m not getting the solution for decimal values and i do not have idea about the how to set different color for multiple lines(i tried for different set of colors but it shows that only for first color )

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