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Saha

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2 years, 343 days
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Error, (in dsolve/numeric/bvp/convertsys...

Saha 80
June 02 2023
0 0

How to clear this Error.

My code is

MVP-RK_Method.mw

Similar numerical solution...

Saha 80
June 02 2023
0 0

@mmcdara 

Thanks a lot .Can the above solution be obtained for this  system of equation.But i get this plot.Is this correct?

Here is the code.

SMMS_1.mw

R,L,C,E Values are not given here. &nbs...

Saha 80
May 07 2023
0 0

R,L,C,E Values are not given here.

 

 

 

 

 

@Carl Love 

@mmcdara  Thank you so much,your s...

Saha 80
April 10 2023
0 0

@mmcdara 

Thank you so much,your suggestions are very useful for me,This can be applied to my problem.

I did'nt get the plot,Please Help...

Saha 80
April 08 2023
0 0

ADM_TRY.mw
 

Thank you for your valuable suggestions to work this problem.I found out Adomian polynomials but i couldn't  plot  the series.
> 

restart
> 

with(LinearAlgebra):
> 

F := proc (x) options operator, arrow; x^2 end proc:
> 

u[0] := 1+t*e^(x+y);

1+t*e^(x+y)

  

(1+t*e^(x+y))^2

 (1)
> 

for n from 0 while n <= 6 do V[n] := (diff(F(sum(lambda^i*u[i], i = 0 .. n)), [`$`(lambda, n)]))/factorial(n) end do:
> 

lambda := 0;

0

 (2)
> 

for i from 0 while i <= n-1 do A[i] := V[i] end do;

(1+t*e^(x+y))^2

  

2*(1+t*e^(x+y))*u[1]

  

u[1]^2+2*(1+t*e^(x+y))*u[2]

  

2*u[1]*u[2]+2*(1+t*e^(x+y))*u[3]

  

u[2]^2+2*u[1]*u[3]+2*(1+t*e^(x+y))*u[4]

  

2*u[2]*u[3]+2*u[1]*u[4]+2*(1+t*e^(x+y))*u[5]

  

u[3]^2+2*u[2]*u[4]+2*u[1]*u[5]+2*(1+t*e^(x+y))*u[6]

 (3)
> 

for n from 0 to 1 do u[n+1] := (1/2)*(int(int(diff(add(u[i], i = 0 .. n), x, x)+diff(add(u[n], i = 0 .. n), y, y), t = 0 .. t), t = 0 .. t))+int(int(A[n], t = 0 .. t), t = 0 .. t) end do;

(1/6)*e^(x+y)*ln(e)^2*t^3+(1/12)*(e^(x+y))^2*t^4+(1/3)*e^(x+y)*t^3+(1/2)*t^2

  

(1/60)*(e^(x+y))^2*ln(e)^2*t^6+(1/10)*((1/8)*e^(x+y)*ln(e)^4+(1/4)*e^(x+y)*ln(e)^2)*t^5+(1/12)*e^(x+y)*ln(e)^2*t^3+(1/252)*(e^(x+y))^3*t^7+(1/6)*((1/30)*(e^(x+y))^2+(2/5)*e^(x+y)*((1/6)*e^(x+y)*ln(e)^2+(1/3)*e^(x+y)))*t^6+(1/5)*((1/12)*e^(x+y)*ln(e)^2+(5/12)*e^(x+y))*t^5+(1/12)*t^4

 (4)
> 

v(t) := sum(u[r]*t^r, r = 0 .. 2);

1+t*e^(x+y)+((1/6)*e^(x+y)*ln(e)^2*t^3+(1/12)*(e^(x+y))^2*t^4+(1/3)*e^(x+y)*t^3+(1/2)*t^2)*t+((1/60)*(e^(x+y))^2*ln(e)^2*t^6+(1/10)*((1/8)*e^(x+y)*ln(e)^4+(1/4)*e^(x+y)*ln(e)^2)*t^5+(1/12)*e^(x+y)*ln(e)^2*t^3+(1/252)*(e^(x+y))^3*t^7+(1/6)*((1/30)*(e^(x+y))^2+(2/5)*e^(x+y)*((1/6)*e^(x+y)*ln(e)^2+(1/3)*e^(x+y)))*t^6+(1/5)*((1/12)*e^(x+y)*ln(e)^2+(5/12)*e^(x+y))*t^5+(1/12)*t^4)*t^2

 (5)
> 

plot(v(t), x = .101 .. .109);

Warning, expecting only range variable x in expression 1+t*e^(x+y)+(1/6*e^(x+y)*ln(e)^2*t^3+1/12*(e^(x+y))^2*t^4+1/3*e^(x+y)*t^3+1/2*t^2)*t+(1/60*(e^(x+y))^2*ln(e)^2*t^6+1/10*(1/8*e^(x+y)*ln(e)^4+1/4*e^(x+y)*ln(e)^2)*t^5+1/12*e^(x+y)*ln(e)^2*t^3+1/252*(e^(x+y))^3*t^7+1/6*(1/30*(e^(x+y))^2+2/5*e^(x+y)*(1/6*e^(x+y)*ln(e)^2+1/3*e^(x+y)))*t^6+1/5*(1/12*e^(x+y)*ln(e)^2+5/12*e^(x+y))*t^5+1/12*t^4)*t^2 to be plotted but found names [e, t, y]

  

 
> 

``


 

Download ADM_TRY.mw

@mmcdara 

@mmcdara  Thank you for your valua...

Saha 80
December 23 2022
0 0

@mmcdara 

Thank you for your valuable suggestions.

I did'nt get the plot,Please Help...

Saha 80
July 01 2022
0 0

I can't plot because sv value is not available,Please help,What to do

> 

restart; with(plots)
> 

eq1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta

 (1)
> 

eq2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x));

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x))

 (2)
> 

params := [M = 1, alpha = 0, eta = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, c[s] = 670, c[f] = 4179, `&rho;&beta;`[s] = 6500, `&rho;&beta;`[fl] = 20939.1, K[s] = 6, K[f] = .613, K[nf] = .6842];

[M = 1, alpha = 0, eta = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, c[s] = 670, c[f] = 4179, `&rho;&beta;`[s] = 6500, `&rho;&beta;`[fl] = 20939.1, K[s] = 6, K[f] = .613, K[nf] = .6842]

  

F(0) = 0, F(1) = val, F(10) = 1, Theta(0) = 1, Theta(10) = 0

 (3)
> 

odesys := eval([eq1, eq2], params);

[diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)), 1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x))]

 (4)
> 

SM := proc (shoot) local ans; if type(shoot, numeric) then ans := dsolve*(eval*([odesys[], bcs], val = shoot), numeric); return rhs(ans(1)[2]) else return 'procname(args)' end if end proc:

fsolve(SM)

 (5)
> 

sol := dsolve*(eval*([odesys[], bcs], val = sv), numeric); sol(1)[1 .. 2]; odeplot*(sol, [[x, f(x)], [x, theta(x)]], x = 0 .. 10, color = [red, blue], legend = [typeset(f(x)), typeset(theta(x))])

Error, (in dsolve) expecting an ODE or a set or list of ODEs. Received 1

  

plots:-odeplot*(dsolve*(eval*([diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)), 1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)), F(0) = 0, F(1) = val, F(10) = 1, Theta(0) = 1, Theta(10) = 0], val = fsolve(SM)), numeric), [[x, f(x)], [x, theta(x)]], x = 0 .. 10, color = [red, blue], legend = [typeset(f(x)), typeset(theta(x))])

 (6)
> 

NULL


 

Download Numeric-Solution.mw

@tomleslie 

@tomleslie Sorry Sir,I typed this i...

Saha 80
June 20 2022
0 0

@tomleslie Sorry Sir,I typed this in Document mode.So it is like this. 

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