Solving ordinary differential equations using the Taylor Series

Abstract

This essay will shed light on some basic knowledge about Taylor Series and ordinary differential equations and then detail the principle and method of using Taylor Formula to solve ordinary differential equations. After analyzing and demonstrating examples, this essay illustrates the feasibility and advantages of the Taylor Formula in solving ordinary differential equations. It points out some problems about Taylor expansion’s convergence speed and computational efficiency. Finally, this paper concludes with the applications of the Taylor Formula to solve ordinary differential equations and prospects for possible future application directions.