MATH 542 NUMERICAL ANALYSIS
FINITE DIFFERENCE METHODS
In this section, each derivative in a differential equation will be replaced by a finite difference approximation leading to an algebraic system. If the original equation was linear the corresponding algebraic system will be linear. Things to remember from Math 541 are the solution methods for linear systems. (Gaussian Elimination and the LU factorization, the Tridiagonal Algorithm, and Iterative Methods like Gauss-Seidel and SOR)
Finite Difference Approximations
Derived using Taylor's Series.
Order of Approximation
BOUNDARY VALUE PROBLEMS(ODE)
Example 1 MATLAB CODE
Example 2 MATLAB CODE
Hanging Cable Problem
MATLAB CODE
Multivariable Newton's Method for solving
non-linear systems
PARTIAL DIFFERENTIAL EQUATIONS
Laplace's Equation MATLAB CODE
Heat Equation MATLAB CODE
Method of Lines
Revised 12/06/04
By Don Short, dshort@sciences.sdsu.edu