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Solving Multi-variable Partial Differential Equation

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Captain Rituraj Singh
评论： Captain Rituraj Singh 2023-10-5
boundary conditions;
Please help me to solve above differential eqation. I want P = P(x,y) and also generate a 3D plot for the same.
I am a new to MATLAB, any help shall be highly appreciated.
Thanks in advance.

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Torsten
Torsten 2023-10-3
编辑：Torsten 2023-10-3
The only thing you can get with the "boundary condition" you gave is the solution on the characteristic curve of the PDE through (x0,y0).
Look up "method of characteristics" for more details.
And I don't understand why you write
I am a new to MATLAB, any help shall be highly appreciated.
It's not a MATLAB problem.
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Torsten
Torsten 2023-10-4
编辑：Torsten 2023-10-4
Ran in:
fun = @(t,u)[cosh(u(2));-sinh(u(2))/u(1);-u(3)/(3*u(1))];
u0 = [0.1;0.1;0.5];
tstart = -10;
tend = 10;
tspan1 = [0 tstart];
[T1,U1] = ode45(fun,tspan1,u0);
tspan2 = [0 tend];
[T2,U2] = ode45(fun,tspan2,u0);
T = [flipud(T1);T2(2:end)];
U = [flipud(U1);U2(2:end,:)];
plot3(U(:,1),U(:,2),U(:,3))
xlabel('x')
ylabel('y')
zlabel('P')

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