A Study on Time Dependent Coordinate Transformation and Its Applications: Efficient Approximation of Nonlinear Partial Differential Equations using Time Dependent Coordinate Transformation

Abstract

Thisresearch is primarily concerned with the use of Time Dependent CoordinateTransformation methods for the approximate solution of nonlinear partialdifferential equations of parabolic type. Such methods have become a popularmeans for the solution of problems which may contain sharp features that arehard to approximate, whilst efficiently managing computational overheads.