Introduction of the differential transform method to solve differential equations at undergraduate level

Abstract

The differential transform method (DTM) and the multi-step differential transform method (MsDTM) are numerical methods that most undergraduate students are not familiar with. The methods provide solutions in terms of convergent series with easily computable components. The aim of this article is to introduce the DTM and MsDTM as efficient tools to solve linear and nonlinear differential equations, at undergraduate level. We choose a population growth problem and a mixing problem to illustrate the simplicity and accuracy of its variants by comparing the results with the Runge–Kutta method.

Keywords:

• numerical methods
• differential transform method
• multi-step differential transform method
• Taylor series