MATLAB: How to solve a nonlinear Parabolic PDE IBVP

nonlinearpde

I am wondering how can I solve the porous medium equation (nonlinear heat equation) in a finite domain in 1D, with Dirichlet type boundary conditions and an initial condition. Matlab's PDE toolbox is still short of performing this task, as far as I know.

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Since the problem is 1D, you can use the pdepe function.

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MATLAB: How to specify boundary conditions on subdomain borders using the Partial Differential Equation (PDE) Toolbox 1.0.13 (R2008b)

One should be able to specify boundary conditions on all external boundaries of any geometry.

 For example, look at the “A scattering problem” example in the documentation. It has a Neumann condition at the outer boundary and a Dirichlet condition at the inner boundary (that is formed by the square sub-region).

Boundary conditions on internal boundaries such as boundaries across which material properties or governing equations might change are not required by Finite Element method.

MATLAB: PDE Parabolic coefficient

Hi,

PDE Toolbox accepts c-matrices in many different forms depending on whether the matrix is symmetric, unsymmetric or diagonal and also whether the coefficients vary as a function of x. This is discussed more on page 5-21 of the manual.

For your scalar case with a full, unsymmetric matrix, c would be: c=[1 3 2 4]'; Note, this is 4 rows with the coefficients entered by column.

Regards,

Bill

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Related Solutions

MATLAB: How to specify boundary conditions on subdomain borders using the Partial Differential Equation (PDE) Toolbox 1.0.13 (R2008b)

MATLAB: PDE Parabolic coefficient

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