Convergent Power Series of and Solutions to Nonlinear Differential Equations

U. Al Khawaja and Qasem M. Al-Mdallal

International Journal of Differential Equations, 2018, vol. 2018, 1-10

Abstract:

It is known that power series expansion of certain functions such as diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of that is convergent for all . The convergent series is a sum of the Taylor series of and a complementary series that cancels the divergence of the Taylor series for . The method is general and can be applied to other functions known to have finite radius of convergence, such as . A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:6043936

DOI: 10.1155/2018/6043936

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