An iterative technique based on HPM for a class of one dimensional Bratu’s type problem

Jyoti, and Mandeep Singh

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 50-64

Abstract: An effective iterative computational technique is developed for the nonlinear initial and boundary value problems and employed on a class of one dimensional Bratu’s type problems. In the proposed technique, we use the homotopy concepts (similar as homotopy perturbation method (HPM)) for the recursive scheme which is obtained in terms of Green’s function with the support of the Picard’s iterative method and boundary/initial conditions. It generates, estimated solutions in the form of series, which is extremely useful in terms of computing. The suggested technique is also subjected to a convergence and error analysis. To highlight the method’s ease of implementation and usefulness, certain numerical examples have been provided and also compared our results with other existing results.

Keywords: Second order nonlinear problem; Bratu-type equation; Homotopy perturbation method; Picard’s method; Green’s function; Convergence analysis (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:50-64

DOI: 10.1016/j.matcom.2022.04.007

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