Which numerical method is more effective for solving parabolic diffusion PDE in 2D [ with Dirichlet boundary conditions, initial condition at time t =0 is given]? The PDE may represent time dependent heat equation in two space variables, an IBVP.
Thanks!
Dear Tekle Gemechu,
Regarding this question, I am sharing my experience here in this area which may be useful.
I would suggest Crank-Nicolson method for solving your Diffusion PDE, due to the enhanced convergence properties through this method. Unfortunately, there is a small problem. As far as the heat transfer equation is concerned, by taking into account the dependency of thermal diffusivity (thermal properties) to the temperature, numerical modeling of the implicit part of the discretized Crank-Nicolson equation will not be so easy. Therefore, as my second suggestion, It is better to use an explicit time discretization and a simple spatial discretization (second-order central finite difference, as it is a diffusion problem).
Regards.
No, my interest is not on numerical. I have interest in analytical part of PDE
Dear Ohiemi Echude,
thanks!
There are cases when we require numerical solutions.
Hi @Tekle Gemechu,
For solving Parabolic PDEs, Finite Difference Method is more easy to apply and to calculate numeral values each at the mesh points of a given problem.
You can use Explicit method to solve parabolic typed of PDEs or Implicit Crank-Nicolson method can be applied for solving these types of equation.
C-N method is unconditionally stable. So, C-N method is more accurate than the explicit method.
I have added my hons. Project to my profile. We have investigate Finite Difference Method for solving Heat Equation, A parabolic Partial Differential Eqaution. You can check it out now.
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