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# Questions tagged [finite-difference-method]

Tag for the usage of "FiniteDifference" Method embedded in NDSolve and implementation of finite difference method (fdm) in mathematica.

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### Reaction diffusion equation

I have an issue when I run this code which illustrates the 2D Fisher KPP equation for boundary condition u=0 and initial condition is equal to 1 if (x,y)=(0,0) and0 otherwise , isue finite diffrence ...
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1 vote
0 answers
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### How to constrain two PDE variables to be the same value on boundary?

I have a 4 pdes for 4 variables: v, v2, ua, and p. I would like to specify that v==v2 on the left and right boundaries at all times. Here are the equations: I discretise the system using PDEtoODE. ...
2 votes
1 answer
223 views

6 votes
1 answer
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### Problem with pdetoode for two coupled PDEs

I tried to adapt a code for a single equation to solve the following system using 'pdetoode' Updated answer ...
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3 votes
1 answer
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### Numerical solution of the Richards' equation

I am trying to solve Richards' equation to model fluid flow in soil. The governing partial differential equation, initial condition, and boundary conditions are: The analytical solution of the ...
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3 answers
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### Generalize the code to more variables

I have this code it runs and gives me the solution. How can I make it more compact and If I want it to extend(generalize) it to more variables how can I do it. I had asked a similar question here (...
• 219
5 votes
2 answers
223 views

### Crafting a replacement rule to convert derivatives to finite differences

I need to construct a replacement rule to replace (first) derivatives with centered finite differences. What I've got so far is ...
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1 vote
1 answer
106 views

### A way to generalize my code for this non linear ODE problem

I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
• 219
1 vote
0 answers
98 views

### Solve system of ODE by fractional finite difference method

I am trying to solve the following system using fractional finite difference method: where e=0.1, a=1.3, m=0.3, p=10, g=3, k=1 and s1, s2, s3 it was mentioned in this paper that it is calculated ...
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6 votes
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1 vote
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### solving ordinary coupled differential equation

I have a set of 8 ordinary differential equations containing matrices which I need to solve using initial conditions. I have written the equations in this form: ...
• 101
1 vote
1 answer
268 views

### NonStandard finite difference for BMBB equation

I am trying to implement the following scheme mentioned in the paper "NUMERICAL SOLUTIONS OF BENJAMIN-BONA-MAHONY-BURGERS EQUATION VIA NONSTANDARD FINITE DIFFERENCE SCHEME " What is ...
0 votes
1 answer
324 views

### Method of lines in a single PDE

After solving this following PDE in NDSolve, now I have to use the method of lines to solve it and then compare the results. I was following the tutorial from Wolfram for Method of lines (https://...
18 votes
1 answer
639 views

### Stable fluids code for electromagnetic mixture application

This code has been translated from the original Jos Stam code and improved with some Mathematica functions. It solves problem of viscous incompressible flow with electromagnetic force in a rectangle ...
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