Taylor Series Method in Numerical Integration: Linear and Nonlinear Problems

Abstract

This article deals with the high-order integration method based on the Taylor series. The paper shows the positive properties of the Modern Taylor Series Method on a set of technical initial value problems. These problems can be transformed into autonomous systems of ordinary differential equations for both linear and nonlinear problems, and the solution can be effectively parallelized. The numerical solution is analyzed and compared with the state-of-the-art solvers.