Nonstandard finite differences for a truncated Bratu–Picard model

Paul Andries Zegeling and Sehar Iqbal

Applied Mathematics and Computation, 2018, vol. 324, issue C, 266-284

Abstract: In this paper, we consider theoretical and numerical properties of a nonlinear boundary-value problem which is strongly related to the well-known Gelfand–Bratu model with parameter λ. When approximating the nonlinear term in the model via a Taylor expansion, we are able to find new types of solutions and multiplicities, depending on the final index N in the expansion. The number of solutions may vary from 0, 1, 2 to ∞. In the latter case of infinitely many solutions, we find both periodic and semi-periodic solutions. Numerical experiments using a non-standard finite-difference (NSFD) approximation illustrate all these aspects. We also show the difference in accuracy for different denominator functions in NSFD when applied to this model. A full classification is given of all possible cases depending on the parameters N and λ.

Keywords: Boundary value problems; Truncated Bratu–Picard model; Multiplicity; Existence; (Non)standard finite differences; Bifurcation diagram (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:324:y:2018:i:c:p:266-284

DOI: 10.1016/j.amc.2017.12.005

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