A Study Of Applied Reduced Differential Transform Method Using Volterra Integral Equations In Solving Partial Differential Equations
Nguyen Minh Tuan

King Mongkut^s University of Technology North Bangkok Thailand

Abstract

Nowadays, integration is one of the trending fields applied in calculus, especially in partial differential equations.
Researchers are trying to support useful utilities to solve partial differential equations in many kinds of methods. In this paper,
we perform an application of Volterra Integral Equations in reduced differential transform method (we call VIE-RDTM) to find
the approximate solutions of partial differential equations. Using the method is to perform the combination of derivative and
integration. The aim is to find the approximate solutions approach to the exact solutions with more general forms. We also extend
some new results for basic functions and compare the solutions using the reduced differential transform method and VIE-RDTM
by depicting the approximate solutions in some partial differential equations. The results showed that the VIE-RDTM method gets
state-of-the-art general form of the solutions when the errors approach to zero.

Keywords: RDTM, VIE-RDTM, integration, derivative, equation

Topic: Mathematics