Finite Difference Methods For Parabolic Equations

Abstract

We present in this thesis the numerical solution to the partial differential equations of parabolic type using the finite-difference methods, namely explicit and Crank-Nicolson methods. We account the local truncation error of the two schemes by using Taylor series and discuss the consistency or compatibility, convergence and stability of these schemes for the parabolic equations. We present vector and matrix norms, also a necessary and sufficient condition for stability. Finally study the stability by the Fourier series method (von Neumann’s method) and use lax’s equivalence theorem to determine the consistency, stability and convergence.