Numerical Methods for Partial Differential Equations

版本 1.0.0.0 (143.6 KB) 作者: Sammit Jain
Numerical Methods for Partial Differential Equations (MATH F422 - BITS Pilani)
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更新时间 2017/11/27
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Numerical Methods for Partial Differential Equations (MATH F422 - BITS Pilani)
How to find your way through this repo:

Navigate to the folder corresponding to the problem you wish to solve.
Clone the entire folder and not just the main .m files, as the associated functions should be present.
Run the code normally in MATLAB, with the following tweaks:
a. Change initial and exact functions according to requirement.
b. Make sure you incorporate changes in the scheme due to different equations.
c. Adjust the mu values based on steps in the dimensions (N and M respectively)

NMPDE is a course offered at BITS Pilani University, which deals with solving PDEs using numerical FD schemes, and studying their respective stabilities and orders of convergence.

Some of the schemes covered are: FTCS, BTCS, Crank Nicolson, ADI methods for 2D Parabolic PDEs, Theta-schemes, Thomas Algorithm, Jacobi Iterative method and Gauss Siedel Method

So far, we have covered Parabolic, Elliptic and Hyperbolic PDEs usually encountered in physics.

In the Hyperbolic PDEs, we encountered the 1D Wave equation and Burger's equation. They were solved using the following schemes:

Lax Friedrichs Scheme
Upwing Scheme
Leap Frog Scheme
Crank Nicolson Scheme
Lax Wendroff Scheme
Gudunov Scheme
The course is a practical introduction to modelling real life problems using partial differential equations and finding approximate solutions using robust, practical numerical methods.

引用格式

Sammit Jain (2024). Numerical Methods for Partial Differential Equations (https://github.com/sammitjain/NMPDE), GitHub. 检索来源 .

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BTCS

CrankNS

EllipticInPolarCoordinates

EllipticPDEs/MyPoisson

EllipticPDEs/PoissonEqn

FTCS

Hyperbolic/MyHyperbolic

Lab_Sheet1_ODE

ParabolicPDEs/NonLinearParabolic

ParabolicPDEs/Parabolic_2D

Practice/Lab1_FTCS

Practice/Lab1_MOL

Practice/Lab2_BTCS

Practice/Lab2_FTCS

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