Solving ordinary differential equations using the Taylor Series
DOI:
https://doi.org/10.61173/k82ntc62Keywords:
Ordinary differential equations, Taylor Formula, Appliances, EvaluationAbstract
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.
References
[1] Moore, R.E Interval analysis. Prentince-Hall, Englewood Cliffs, N.G., 1966.
[2] Rall, L.B. Automatic Differentiation: Techniques and Applications Lecture Notes in Computer Science, Vol 120, Springer-Verlag, New York, 1981.
[3] Example:1-9 From baijiahao.baidu.com/s?id=1657057073 012577784&wfr=spider&for=pc
[4] Example:10-15 from zhuanlan.zhihu.com/p/433180918 by Matlab Fans, published on 14 November 2021.
[5] Runge-Tutta Formulas: In numerical analysis, Runge-Kutta methods are an important class of implicit or explicit iterative methods for solving nonlinear ordinary differential equations. These technologies were invented by mathematicians Carl Runge and Martin Wilhelm Kutta around 1900.
[6] Difference method: a numerical method for differential equations approximating derivatives through finite difference methods, thereby seeking approximate solutions to differential equations.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 by the authors.
This work is licensed under a Creative Commons Attribution 4.0 International License.
