Solving Cauchy problem for first order PDE
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How to solve the following Cauchy problem using MATLAB: x*U_x + y*U_y = U+1; U(x,y)= x^2 on y= x^2
I was trying using the following command: dsolve('Dx=x','Dy=y','Du=u+1');
But the problem is how to apply Cauchy data? Please advice.
2 个评论
John D'Errico
2017-2-12
What Cauchy data? You have not shown any data.
As well, you might also explain what you intended by the expression:
U+!
Akansha Mittal
2017-2-13
回答（1 个）
There is no ready-to-use MATLAB program to solve this kind of problem.
I suggest you look up "method-of-characteristics". Your PDE can be solved analytically.
Best wishes
Torsten.
3 个评论
Akansha Mittal
2017-2-13
Don't know if it works, but you'll see how to proceed:
syms x(s) y(s) u(s) X0
[solx,soly,solu] = dsolve(diff(x,s)==x, diff(y,s)==y, diff(u,s)==u+1, x(0)==X0, y(0)==X0^2, u(0)==X0^2);
[X0sol,ssol]=solve([solx==x,soly==y],[X0,s]];
subs(solu,[X0,s],[X0sol,ssol])
Best wishes
Torsten.
naren BORO
2022-6-30
programming is not correct
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2017-2-12
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