The Finite Difference Methods for Hyperbolic – Parabolic Equations

The objective of this paper is to construct numerical schemes using finite difference methods for the one-dimensional general hyperbolic- parabolic- reaction problem.
The finite difference method with the exponential transformation form is used to solve the problem, and employs difference approximation technique to obtain the numerical solutions. Computational examples are presented and compared with the exact solutions. We obtained that the Crank-Nicholson scheme is more accurate than Forward scheme. Therefore the form of exponential transformation for the problem yields a stable solution compared with exact solution.