A New Taylor Series based Numerical Method: Simple, Reliable, and Promising

Abstract

Taylor series method is a simple analytical method, which is accessible to all non-mathematician, has slow convergence. This paper develops a new Taylor series based numerical method to overcome the shortcoming of the Taylor series while maintaining its simplicity. Some examples are given, showing its reliability and efficiency. The proposed method is also proved to be extremely effective for initial value problems and boundary value problems. The method provides a universal approach to various highly non-linear problems, and it sheds a bright light on numerical theories for practical engineering applications.

Keywords

• taylor series
• singular boundary value problem
• kdv equation
• burgers' equation
• system of burgers equation