Arbitrary-order numerical schemes for model parabolic equation

Abstract

This report investigates the general theory and methodology of high order numerical schemes for one-dimensional model parabolic equation. The Universal Formula from which a 2-level explicit arbitrary-order numerical methods for diffusion equation can be derived is developed. Using the Universal Formula some high order numerical methods are constructed. Some important features of numerical methods are revealed through the construction of high order numerical methods and stability analysis. Subject to the limitation of diffusion number, d, being positive, only the method that satisfies positive stable region is relevant.