Numerical Solution: Partial Differential Equations

 

 

1D Wave Equation

 

Solution

 

 

 

1D Diffusion Problem

 

Explicit Finite Difference Scheme

 

detlaT = 0.5

 

1) Total Time = 100*0.5 time unit. Gif is first 10 snapshot and then every subsequent 10 time unit

 

2) Total Time = 200000*0.1 time unit. Gif is first 10 snapshot and then every subsequent 1000 time unit.

 

 

 

deltaT = 0.1

 

1) Total Time = 500*0.1 time unit. Gif is first 10 snapshot and then every subsequent 10 time unit

 

2) Total Time = 1000000*0.1 time unit. Gif is first 10 snapshot and then every subsequent 1000 time unit.

 

 

 

 

 

 

Implicit Finite Difference Scheme

 

(something is wrong)

 

 

 

2D Diffusion Problem

 

 

 

 

Laplace Equation in 2D