# Questions tagged [finite-difference]

Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.

791 questions
Filter by
Sorted by
Tagged with
1 vote
51 views

### Advection diffusion equation using Crank-Nicolson with total flux and Diriclet BCs

I am trying to model the 1D advection-diffusion equation: $${\partial c \over \partial t} = D_c{\partial^2 c \over \partial x^2} -u{\partial c \over \partial x}.$$ With Robin boundary conditions that ...
• 51
1 vote
334 views

### How to solve heat equation in spherical coordinates with finite differences?

I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only. ...
• 111
1 vote
91 views

1 vote
52 views

### Stability plot of upward difference implicit time

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. Im asking if those stability ...
152 views

### Discretization of a non-linear ODE using FDM isn't grid indepenent

I am trying to solve the ODE : $\frac{d^2T}{dx^2} = \omega_1 T+\omega_2 T^2$ + using different numerical methods. I have tried the following discretizations so far and none of them seem to be grid ...
1 vote
56 views

• 255
515 views

### Trouble Implementing 1d Wave Equation Finite Difference Solver

Im trying to solve the 1d Wave Equation on $x \in \mathbb{R}, t > 0$: $$u_{tt} = c^2u_{xx}, \hspace{5mm} u(x,0) = \cos(4 \pi x), \hspace{5mm} u_t(x,0) = 0$$ with $c = 1$ and a periodic boundary ...
• 123
89 views

### Divergence on wave equation simulation

I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
137 views

### Incorporating heat flux into Laplace Equation

I need to find the temperature distribution of a square plate using the Laplace equation by using FDM: $$\frac{d^2T}{dx^2} + \frac{d^2T}{dy^2} = 0$$ But there is a heat flux entering from the top ...
• 145
1 vote