Questions tagged [finite-difference-method]
Tag for the usage of "FiniteDifference" Method embedded in NDSolve and implementation of finite difference method (fdm) in mathematica.
152 questions
0 votes
0 answers
158 views
Performance of solving time-fractional convection in a square cavity using finite-difference method
Here we give three tests for the problem of natural convection of air in a rectangular cavity with a Rayleigh number of $Ra=10^4$ and with the time-fractional derivative $\partial_t^{\alpha}$ in the ...
- 52.2k
5 votes
2 answers
768 views
IBVP of PDE system deduced from Kirchhoff's rod theory
I am trying to solve the following system of nonlinear PDEs in Mathematica, but I'm encountering difficulties, particularly with defining the initial conditions. Here's the system I am working with: $$...
- 366
2 votes
0 answers
75 views
pdetoode for heat equation with Neumman bc without NeumannValue
I want to try pdetoode for solving a heat equation with Neumman bc without using NeumannValue. I modified this code: ...
- 245
7 votes
3 answers
1k views
Numerical solution of Burgers' equation
I am trying to solve Burgers' equation $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}-\frac{1}{100\pi}\frac{\partial^2u}{\partial x^2}=0$$ subject to conditions $u(x,0)=-\sin(\pi x)$ ...
- 357
1 vote
1 answer
351 views
Solving a 6th-Order PDE Numerically?
I try to solve f(x,t) numerically. Actually, this figure obtained employing pathlength continuation techniques as bundled in auto07p (or more modern pde2path) by Matlab So any help to NDSolve by ...
6 votes
0 answers
134 views
Bathtub vortex simulation with Mathematica FEM
Bathtub vortex is well known phenomena that can be simulated with numerical methods like FDM described here and FEM described in our paper here. Let consider bath with 2 inlets and one outlet in a ...
- 52.2k
8 votes
2 answers
637 views
Boundary condition for heat equation in polar coordinates deduced with L'Hôpital's rule fails for method of lines, but works well for FDM
Update I manage to find a way that resolves the problem. I'd like not to make this solution public for the moment so other answerers will have more chance to get the bounty. Here's a hint: it's a ...
- 71.5k
4 votes
0 answers
206 views
Issues in Reproducing Rippling Instability of Graphene using Mathematica from Physical Review B 101, 235428 (2020)
I'm attempting to reproduce the numerical model of the rippling instability of graphene as described in the paper "Physical Review B 101, 235428 (2020)" using Mathematica. Specifically, I'm ...
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