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A new coupled reduced alternating group explicit method for nonlinear singular two-point boundary value problems on a variable mesh

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Abstract

In this paper, we discuss a new coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to solve the nonlinear singular two-point boundary value problems u″ = f(r, u, u′), 0 < r < 1 subject to given natural boundary conditions u(0) = A 1, u(1) = A 2 where A 1 and A 2 are finite constants, along with a third-order numerical method on a geometric mesh. The proposed method is applicable to singular and nonsingular problems. We have discussed the convergence of the CRAGE iteration method in detail. The results obtained from the proposed CRAGE iteration method are compared with the results of the corresponding two-parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, South Asian University Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India

    R. K. Mohanty

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110 007, India

    J. Talwar

Authors
  1. R. K. Mohanty
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  2. J. Talwar
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Correspondence to R. K. Mohanty.

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Original Russian Text © R.K. Mohanty, J. Talwar, 2015, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2015, Vol. 18, No. 1, pp. 65–78.

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Mohanty, R.K., Talwar, J. A new coupled reduced alternating group explicit method for nonlinear singular two-point boundary value problems on a variable mesh. Numer. Analys. Appl. 8, 55–67 (2015). https://doi.org/10.1134/S1995423915010061

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  • DOI: https://doi.org/10.1134/S1995423915010061

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