# Questions tagged [pdepe]

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### Form of nonlinear diffusion equation

Consider the following nonlinear diffusion problem, $$\frac{\partial u}{\partial t} = x^{-2}\frac{\partial}{\partial x}\left(x^2 u^4 \frac{\partial u}{\partial x}\right), \quad 0 < x < 1$$ We ...
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### How do I use pdepe for a first order parabolic PDE with only one boundary condition?

I am trying to use Matlab's pdepe.m to solve the first order parabolic PDE $$\frac{\partial u}{\partial x}+\frac{\partial u}{\partial x}=x$$ I have not had trouble coding the argument of pdepe @pdefun:...
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### Simulating 1D diffusion

I'm trying to understand the influence of Neumann boundary condition while simulating 1D diffusion equation $$\frac{\partial C}{\partial t} = \nabla \cdot (D \nabla C).$$ The initial value is set ...
I'm solving the following 1D transport equation in MATLAB's pdepe solver. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ At the inlet (left ...
I'm interested in studying the effect of mesh size on the behavior of the solution curves of 1D convection-diffusion problem. \frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - ...