Solving Multi-variable Partial Differential Equation
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Captain Rituraj Singh
on 3 Oct 2023
Commented: Captain Rituraj Singh
on 5 Oct 2023
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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Accepted Answer
Torsten
on 3 Oct 2023
Edited: Torsten
on 3 Oct 2023
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.
6 Comments
Torsten
on 4 Oct 2023
Edited: Torsten
on 4 Oct 2023
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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