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Bernstein Collocation Method for Solving High-Order Singular Differential–Difference Equations

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Abstract

The purpose of this article is to present an efficient numerical approach based on Bernstein polynomials for solving high-order linear singular differential–difference equations, linear Lane–Emden type differential equations. Apart from these equations, high-order nonlinear singular Emden–Fowler type equations of tricky nature have been considered to study the nature of the approximate solutions using proposed method. The unknown Bernstein coefficients in approximate solution are obtained using collocation points. The results of numerical experiments on some test problems confirm the accuracy and efficiency of our approach. The proposed method can easily be performed computationally in less time.

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Authors and Affiliations

  1. Department of Mathematics, Government College for Men(A), Kadapa, Andhra Pradesh, India

    V. Appalanaidu

  2. Department of Mathematics, UCEK, JNTUK, Kakinada, Andhra Pradesh, India

    G. V. S. R. Deekshitulu

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  1. V. Appalanaidu
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  2. G. V. S. R. Deekshitulu
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Appalanaidu, V., Deekshitulu, G.V.S.R. Bernstein Collocation Method for Solving High-Order Singular Differential–Difference Equations. Int. J. Appl. Comput. Math 9, 12 (2023). https://doi.org/10.1007/s40819-023-01492-9

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