Coupling of ¬¬Laplace Differential Transform method with Padé Approximant for the Numerical solution of Initial and Boundary value problems

Abstract

This paper presents a study using a novel linearization technique based on the Differential transformation method (DTM) to seek analytical solutions if it exists and approximate solutions where closed form solutions are not available. The effectiveness and accuracy of this procedure is verified by solving six problems comprising both initial and boundary value problems by a combination of DTM and Laplace transform method. The resulting solution is then treated with Padé approximation to obtain a better approximation that converges to the exact solution. Simulated results of the study reveal the proposed technique is reliable, accurate and computationally convenient even with few iterations. The result obtained is in good agreement with existing literature.