Maple 13 Questions and Posts

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

  how can I find equation discribing elliptic intersections and use lagrange to show the higest and lowest value ?    g 

I am trying to solve the particular system of partial differential equation. But I get the following error.pdsolve.mw
 

"restart;  f(x,y):=x*y:  yy:={diff(f(x,y),x)=0,diff(f(x,y),y)=0}:  ee:=pdsolve(yy,numeric);"

Error, (in pdsolve/numeric) invalid subscript selector

 

``


 

Download pdsolve.mw

 

I am trying to evaluate the following double integral where hypergeom([x,1/2],[3/2],C) is gauss hypergeometric function 2f1. maple gives back it unevaluated. I doubt it may be due to slow convergence of hypergeometric function. 
 

restart; x := (1/6)*Pi; evalf(int(evalf(int(cos(x)*hypergeom([x, 1/2], [3/2], sin(x)/(r*cos(x)+k-2*r*sin(x))^2)/(r*sin(x)^2+r*cos(x)+k)^4, k = 0 .. 10)), r = 1 .. 2))

Int(Int(.8660254040*hypergeom([.5000000000, .5235987758], [1.500000000], .5000000000/(-.1339745960*r+k)^2)/(1.116025404*r+k)^4, k = 0. .. 10.), r = 1. .. 2.)

(1)

``


 

Download DOUBLE_INT_2.mw

I am trying to evaluate the following triple integral but it takes much time so i kill the job.


 

restart; R := 5; KK := proc (theta) options operator, arrow; evalf(int(int(int(1/(R*sin(theta)^2+(R*cos(theta)+Z)^2+(2*R*k.sin(theta))*cos(p))^2, p = 0 .. 2*Pi), Z = 0 .. 60), k = 1 .. 10, numeric)) end proc; evalf(KK((1/6)*Pi))

Warning,  computation interrupted

 

``


 

Download int_maple_prime2.mw

 

Dear sir,

in the program boundary conditions D(f)(0)=0 doesn't showing result but when use d(f)(0)=1 it will execute, why is this can you explain this ?program.mw
 

Hi Mapleprimes,

We know that '' rsolve '' is a recurrence equation solver.  It is more than an expression simplifier.

Congratulations to the Maple computer algebra team for creating such a great computer tool.  simply want to know more.

rsolve_on_May_16_2017.pdf

Surely there are many steps to determine the values to place.

Regards,

Matt

 

Dear please check once it showing an error program.mw as intial value is not conververging

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.

 

> 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

 

 

 

 

 

> 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 ??

 

hy

i have to develop a code i which i have system of nonlinear equation 

i have to generate the matrix of that nonlinear equation then i want to do or apply any method say newton method and make a loop which help us to find a solution using some tolerance 

at the end i get a result in form of a table which give nth matrix then value of function matrix at nth value then error i-e xn-x(n-1) 

thanx in advance

if i m working in maple 13 i have to solve a non linear integral equation then what will be the steps to use the do loop.

i want a scheme of fractional differential equation so that i solve my questions and make a code of it.

please provide me the scheme

Dear Maple researchers

 

I have a problem in solving a system of odes that resulted from discretizing, in space variable, method of lines (MOL).

The basic idea of this code is constructed from the following paper:

http://www.sciencedirect.com/science/article/pii/S0096300313008060

If kindly is possible, please tell me whas the solution of this problem.

With kin dregards,

Emran Tohidi.

My codes is here:

> restart;
> with(orthopoly);
print(`output redirected...`); # input placeholder
> N := 4; Digits := 20;
print(`output redirected...`); # input placeholder

> A := -1; B := 1; rho := 3/4;
> g1 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(A-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc; g2 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(B-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> f := proc (x) options operator, arrow; 1/2+(1/2)*tanh((1/2)*x/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> uexact := proc (x, t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(x-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> basiceq := simplify(diff(uexact(x, t), `$`(t, 1))-(diff(uexact(x, t), `$`(x, 2)))+uexact(x, t)*(1-uexact(x, t))*(rho-uexact(x, t)));
print(`output redirected...`); # input placeholder
                                      0
> alpha := 0; beta := 0; pol := P(N-1, alpha+1, beta+1, x); pol := unapply(pol, x); dpol := simplify(diff(pol(x), x)); dpol := unapply(dpol, x);
print(`output redirected...`); # input placeholder
> nodes := fsolve(P(N-1, alpha+1, beta+1, x));
%;
> xx[0] := -1;
> for i to N-1 do xx[i] := nodes[i] end do;
print(`output redirected...`); # input placeholder
> xx[N] := 1;
> for k from 0 to N do h[k] := 2^(alpha+beta+1)*GAMMA(k+alpha+1)*GAMMA(k+beta+1)/((2*k+alpha+beta+1)*GAMMA(k+1)*GAMMA(k+alpha+beta+1)) end do;
print(`output redirected...`); # input placeholder
> w[0] := 2^(alpha+beta+1)*(beta+1)*GAMMA(beta+1)^2*GAMMA(N)*GAMMA(N+alpha+1)/(GAMMA(N+beta+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for jj to N-1 do w[jj] := 2^(alpha+beta+3)*GAMMA(N+alpha+1)*GAMMA(N+beta+1)/((1-xx[jj]^2)^2*dpol(xx[jj])^2*factorial(N-1)*GAMMA(N+alpha+beta+2)) end do;
print(`output redirected...`); # input placeholder
> w[N] := 2^(alpha+beta+1)*(alpha+1)*GAMMA(alpha+1)^2*GAMMA(N)*GAMMA(N+beta+1)/(GAMMA(N+alpha+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for j from 0 to N do dpoly1[j] := simplify(diff(P(j, alpha, beta, x), `$`(x, 1))); dpoly1[j] := unapply(dpoly1[j], x); dpoly2[j] := simplify(diff(P(j, alpha, beta, x), `$`(x, 2))); dpoly2[j] := unapply(dpoly2[j], x) end do;
print(`output redirected...`); # input placeholder
print(??); # input placeholder
> for n to N-1 do for i from 0 to N do BB[n, i] := sum(P(jjj, alpha, beta, xx[jjj])*dpoly2[jjj](xx[n])*w[i]/h[jjj], jjj = 0 .. N) end do end do;
> for n to N-1 do d[n] := BB[n, 0]*g1(t)+BB[n, N]*g2(t); d[n] := unapply(d[n], t) end do;
print(`output redirected...`); # input placeholder
> for nn to N-1 do F[nn] := simplify(sum(BB[nn, ii]*u[ii](t), ii = 1 .. N-1)+u[nn](t)*(1-u[nn](t))*(rho-u[nn](t))+d[nn](t)); F[nn] := unapply(F[nn], t) end do;
print(`output redirected...`); # input placeholder
> sys1 := [seq(d*u[q](t)/dt = F[q](t), q = 1 .. N-1)];
print(`output redirected...`); # input placeholder
[d u[1](t)                                                                
[--------- = 40.708333333333333334 u[1](t) + 52.190476190476190476 u[2](t)
[   dt                                                                    

                                                                  2          3
   + 39.958333333333333334 u[3](t) - 1.7500000000000000000 u[1](t)  + u[1](t)

   + 7.3392857142857142858

   - 3.6696428571428571429 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) - 3.6696428571428571429 tanh(
                                                     d u[2](t)   
-0.35355339059327376220 + 0.12500000000000000000 t), --------- =
                                                        dt       
-20.416666666666666667 u[1](t) - 25.916666666666666667 u[2](t)

                                                                  2          3
   - 20.416666666666666667 u[3](t) - 1.7500000000000000000 u[2](t)  + u[2](t)

   - 3.7500000000000000000

   + 1.8750000000000000000 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) + 1.8750000000000000000 tanh(
                                                     d u[3](t)                
-0.35355339059327376220 + 0.12500000000000000000 t), --------- = 29.458333333\
                                                        dt                    

  333333333 u[1](t) + 38.476190476190476190 u[2](t)

                                                                  2          3
   + 30.208333333333333333 u[3](t) - 1.7500000000000000000 u[3](t)  + u[3](t)

   + 5.4107142857142857144

   - 2.7053571428571428572 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) - 2.7053571428571428572 tanh(
                                                   ]
-0.35355339059327376220 + 0.12500000000000000000 t)]
                                                   ]
> ics := seq(u[qq](0) = evalf(f(xx[qq])), qq = 1 .. N-1);
print(`output redirected...`); # input placeholder
    u[1](0) = 0.38629570659055483825, u[2](0) = 0.50000000000000000000,

      u[3](0) = 0.61370429340944516175
> dsolve([sys1, ics], numeic);
%;
Error, (in dsolve) invalid input: `PDEtools/sdsolve` expects its 1st argument, SYS, to be of type {set({`<>`, `=`, algebraic}), list({`<>`, `=`, algebraic})}, but received [[d*u[1](t)/dt = (20354166666666666667/500000000000000000)*u[1](t)+(13047619047619047619/250000000000000000)*u[2](t)+(19979166666666666667/500000000000000000)*u[3](t)-(7/4)*u[1](t)^2+u[1](t)^3+36696428571428571429/5000000000000000000-(36696428571428571429/10000000000000000000)*tanh(1767766952966368811/5000000000000000000+(1/8)*t)-(36696428571428571429/10000000000000000000)*tanh(-1767766952966368811/5000000000000000000+(1/8)*t), d*u[2](t)/dt = -(20416666666666666667/1000000...

How difficult is it to simulate gravitational influences and perturbing effects on celestial orbits with Maple? Could this syntax http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html be altered without excessive changes to consider these aspects?

Are there somewhere worksheets to take a look at as an introduction and to see how such goals would be approached and implemented?

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