shakuntala

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 Anyone can explain to me this program using Runge Kutta fourth order method

Download program.mwprogram.mw

Anyone can explain to me the Runge Kutta method using the following equations and conditions??

 

diff (diff (diff (f (eta), eta), eta), eta)+ f (eta)* diff (diff (f (eta), eta), eta)=0

diff (diff (theta (eta), eta), eta)+ f (eta)* diff (theta (eta), eta)=0

f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1

theta(0) = 1, theta(5) = 0

MHD_cchf_2.mw
 

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w := .572433:

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for j to nops(N, m) do sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+w*x(f(eta)*(diff(diff(f(eta), eta), eta))-(m[j]*m[j])*(diff(f(eta), eta))-(diff(f(eta), eta))^2) = 0, y*(diff(diff(theta(eta), eta), eta))/(pr*z)-b*f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))-b*f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta)) = 0, f(0) = N[j], (D(f))(0) = 1, (D(f))(20) = 0, theta(0) = 1, theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); plots[odeplot](sol1, color = red); plots[odeplot](sol1, [eta, theta(eta)], color = K[j], linestyle = L[j]); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed, linestyle = L[j]); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = box, linestyle = L[j]) end do; plots:-display([seq(fplt[j], j = 1 .. nops(N, m))]); plots:-display([seq(tplt[j], j = 1 .. nops(N, m))])

Error, invalid input: nops expects 1 argument, but received 2

 

Error, invalid input: nops expects 1 argument, but received 2

 

Error, invalid input: nops expects 1 argument, but received 2

 

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Download MHD_cchf_2.mw

 

Respected sir, I try to plot graphs using two parameters once. But it showing the error as

Error, invalid input: nops expects 1 argument, but received 2
Error, invalid input: nops expects 1 argument, but received 2
Error, invalid input: nops expects 1 argument, but received 2

can anybody do help in this regard?

 

Hi everyone, now I try to plot a graph by varying more than one variable. Is it possible to vary for more than one variable at a time (vary the two or more variable at one once) Please anybody can help in this regard?
 

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w := .572433:

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for j to nops(N) do sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+w*x(f(eta)*(diff(diff(f(eta), eta), eta))-(m*m)*(diff(f(eta), eta))-(diff(f(eta), eta))^2) = 0, y*(diff(diff(theta(eta), eta), eta))/(pr*z)-b*f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))-b*f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta)) = 0, f(0) = N[j], (D(f))(0) = 1, (D(f))(20) = 0, theta(0) = 1, theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); plots[odeplot](sol1, color = red); plots[odeplot](sol1, [eta, theta(eta)], color = K[j], linestyle = L[j]); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed, linestyle = L[j]); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = box, linestyle = L[j]) end do:

 

 

sol1(0)

[eta = 0., f(eta) = HFloat(29.999999999999986), diff(f(eta), eta) = HFloat(0.9999999999999996), diff(diff(f(eta), eta), eta) = HFloat(7.515045554999997), theta(eta) = HFloat(0.9999999999999996), diff(theta(eta), eta) = HFloat(-0.42693869190857225)]

(1)

odeplot(sol1, [x, y(x)], -4 .. 4, numpoints = 25)

odeplot(sol1, [1.32156, 5.29387], -4 .. 4, numpoints = 25)

(2)

 

 

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Download MHD_cchf.mw
 

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w := .572433:

``

for j to nops(N) do sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+w*x(f(eta)*(diff(diff(f(eta), eta), eta))-(m*m)*(diff(f(eta), eta))-(diff(f(eta), eta))^2) = 0, y*(diff(diff(theta(eta), eta), eta))/(pr*z)-b*f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))-b*f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta)) = 0, f(0) = N[j], (D(f))(0) = 1, (D(f))(20) = 0, theta(0) = 1, theta(20) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); plots[odeplot](sol1, color = red); plots[odeplot](sol1, [eta, theta(eta)], color = K[j], linestyle = L[j]); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed, linestyle = L[j]); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = box, linestyle = L[j]) end do:

 

 

sol1(0)

[eta = 0., f(eta) = HFloat(29.999999999999986), diff(f(eta), eta) = HFloat(0.9999999999999996), diff(diff(f(eta), eta), eta) = HFloat(7.515045554999997), theta(eta) = HFloat(0.9999999999999996), diff(theta(eta), eta) = HFloat(-0.42693869190857225)]

(1)

odeplot(sol1, [x, y(x)], -4 .. 4, numpoints = 25)

odeplot(sol1, [1.32156, 5.29387], -4 .. 4, numpoints = 25)

(2)

 

 

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Download MHD_cchf.mw

 

 Dear Sir,

I trying to merge two which are one is an actual plotted graph and another one zoomed from the same graph. I want to copy zoomed graph into an actual graph, can anyone help in this regard?

My actual graph is like as follows

and after zooming this graph I got as follows

Now I want to change (Insert the zoomed graph inside the actual graph where the text is inserted) by using these two graphs as below

Please help me to plot like this...

 

 

Dear sir

 I am facing the problem with executing the program with Maple13. The software problem is maple13 is not executing the programs and showing the dialogue box as waiting for the kernel. Actually, what is this kernel, which is not understanding me? So please can anyone do a favor in this regard? How to connect to the kernel? 

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