Analysis of the properties of a derived one-step numerical method of a transcendental function

Abstract

The paper presents a new numerical method for the solution of Initial Value Problems (IVPs) of first order Ordinary Differential Equations (ODEs) via a transcendental basis function. FORTRAN 95 programing language was used for the implementation of the derived numerical scheme. The analysis of the properties of the newly derived method was investigated which includes the stability, accuracy and consistency through which the suitability of it was established. This scheme avoids the need for higher derivative of differential equation. This scheme was tested on some illustrative examples and the results compared favourably with exact solutions. We conclude that the derived numerical method is consistent, convergent, quite stable and more accurate for application to numerical problems and can be widely used in solving first order IVPs in ODEs.

Subject Classification: (2010):

• 31A35
• 34A12
• 35F10

Keywords:

• Accuracy
• Consistency
• Initial value problem
• Differential equation
• Stability