MATLAB: Laplace Equation with pdepe command

MATLABpdepe laplace equation

Hi, I am learning to solve PDEs with pdepe command. First, I try to solve a Laplace equation (1D) setting zero the right coefficients in the PDE. I am expecting the solution to be e.g. y=m*x + b. However I get curves and not lines and I do not know why. I attach the M-files below.

Thanks.

Best Answer

Setting s=1, the solution is of the form u(x)=-1/2*x^2+a*x+b.

Best wishes

Torsten.

Related Solutions

MATLAB: Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.

Your boundary conditions for u2 (q=0, p=0 at each end) are not valid.

The second equation in your system (u2_t=...) is, in fact, a PDE, not an ODE because the RHS contains u1_x which is a function of x. So u2 must be a function of both t and x.

I believe that the second component of your flux, -kn * u(2) * u(1), is also incorrect and that the corresponding term from the second PDE should be included in s. Once you have made this fix, you can define BC on u2 at each end as q=1,p=0. Since f for this PDE will be zero, this BC does nothing but it does satisfy pdepe.

MATLAB: Solving partial differential system

s= [-v*DuDx(1)-psi*km*(qe-u(2)); km*(qe-u(2))];
function [pl,ql,pr,qr] = pdex4bc(xl,ul,xr,ur,t)
Q=2.5; %mL min^-1
A_c=1.96e-5; %cm^2
u=Q/A_c;
e_b=0.368;
v=u/e_b;
pu2 = ?;
pl = [ul(1)-pu2; 0.0];
ql = [-1/v; 1.0];
pr = [0; 0];
qr = [1.0; 1.0];

Best Answer

Related Solutions

MATLAB: Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.

MATLAB: Solving partial differential system

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