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Ordinary Differential Equations of Higher Order Can Always Be Reduced to a Set of First-Order Differential Equations (See, for Example, Reference [1]).

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• TITLE: Numerical Solution of Differential Equations by Direct Taylor Expansion

  AUTHORS: Pirooz Mohazzabi, Jennifer L. Becker

  KEYWORDS: Taylor Series, Expansion, Algorithm, Numerical Solution, Differential Equations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.3, March 22, 2017

  ABSTRACT: A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.