An efficient iterative method for solving Bratu-type equations

In this paper, an efficient analytical iterative method is introduced for solving the initial value and boundary value Bratu problems. A quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear Bratu equations to a sequence of linear problems. An opt...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-09, Vol.357, p.71-84
Main Authors: Tomar, Saurabh, Pandey, R.K.
Format: Article
Language:English
Subjects:
Bratu’s problem
Iterative methods
Picard’s method
Quasilinearization
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Summary:In this paper, an efficient analytical iterative method is introduced for solving the initial value and boundary value Bratu problems. A quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear Bratu equations to a sequence of linear problems. An optimal Picard iteration method is used to obtain approximate analytical solution of linearized versions of Bratu’s equations. The numerical results presented the effectiveness and high performance of the proposed method and comparisons are made with many other existing numerical solution techniques. The comparisons reveal the efficiency and applicability of the present work.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2019.02.025