ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Bernstein Collocation Approach for Solving Nonlinear Differential Equations with Delay and Anticipation

Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 425--434 | DOI:10.5890/DNC.2022.09.006

V. Appalanaidu$^1$, G.V.S.R. Deekshitulu$^2$

$^1$ Department of Mathematics, Govt. college for Men(A), Kadapa, A.P., India

$^2$ Department of Mathematics, UCEK, JNTUK, Kakinada, A.P., India

Abstract

In this paper, the solutions of high-order nonlinear differential equations with delay and anticipation subject to mixed conditions are obtained by converting them into algebraic equations by using Bernstein polynomials and collocation points. Then the algebraic equations are solved by using Newton's method. Some examples are presented to illustrate the method proposed. In the problems involving delay and anticipation, the terms involving deviated arguments are converted into linear terms with the help of Taylor's series.

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