Differential Transform Method in General Orthogonal Curvilinear Coordinates

Abstract

Many real world problems are governed by non-linear differential equations. These may be single or system of ordinary or partial differential equations. In practice, problems involving single differential equations are mostly solved using analytical procedures, while those with systems of equations are solved numerically. A semi-analytical procedure namely Differential Transform Method (DTM) obtained from Taylor series in Cartesian co-ordinates is being used to solve linear or nonlinear equations in practice. This paper introduces the Taylor series and DTM for general orthogonal curvilinear co-ordinates and focuses mainly on DTM in standard two-dimensional polar co-ordinates and three-dimensional cylindrical polar and spherical polar coordinates.