# Tagged Questions

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### Space-dependent diffusivity and finite-differences

I want to implement a finite difference code of this simple diffusion equation with space-dependent diffusivity: $$\partial_{t}u =D\partial_{x}^{2}u+\partial_{x}D\cdot\partial_{x}u$$ I go for a ...
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### Is there a software to solve variational problem using finite difference? [on hold]

I am looking for a software to solve the variational problem. I have formulated it using PDES. I want to use finite difference method. Preferably academic or commercial software for this. ...
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### Finite Difference Spacing of Points for PDE's for Convergence of Explicit Forward-Stepping Scheme

I realize that this question could be pretty broad, but I'm wondering at least what the conditions are for my simulation. I'm developing an Explicit Forward-Stepping Finite Difference scheme to solve ...
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### heat equation with Interface Crank Nicolson

I am currently working on solving the heat equation with an interface numerically using Crank-Nicolson. There are jump discontinuities at the interface which are dealt with using fictitious values ...
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### Reference for Finite Difference Schemes

Is there any place that I can find a list of different PDEs and common finite difference schemes used for each? I have seen tables of finite difference coefficients such as the one here ...
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### Stability of pde in some $L^p$ norm and stability of a numerical scheme for it equivalence.

I would like to get some light on how to proceed and my confusion. I consider some IBVP of the form $$u_t+L(t,x)u=0, x\in D, t\in [0,T]$$ with some BC and initial data. And I use some numerical method ...
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### Harmonic functions and conformal mappings

I would like to get some insight into the practicalities of applying conformal mapping techniques for the numerical solution of PDEs. Up until now I had the impression that conformal mapping ...
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### Orthogonal vs general curvilinear coordinates

Solutions to PDEs over irregular domains can be computed using the finite difference method by the introduction of so called body fitted coordinate systems where the coordinate lines are aligned to ...
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### How do I solve this pde (using finite differences)?

How do I solve the pde: $\ -s_x(x,t) -p(x,t)s_t(x,t)=p(x,t)$ for s(x,t) when p(x,t)=2x, subject to the condition s(0,t)=0? Generally p(x,t) may not be analytical so I would like to use finite ...