Discontinuity, Nonlinearity, and Complexity
Bernstein Collocation Approach for Solving Nonlinear Differential Equations with Delay and Anticipation
Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 425434  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
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Abstract
In this paper, the solutions of highorder 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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