Modified asymptotic solutions for second-order nonlinear singularly perturbed boundary value problems

Chein-Shan Liu and Chih-Wen Chang

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 193, issue C, 139-152

Abstract: We introduce a coordinate transformation of independent variable, such that the second-order nonlinear singularly perturbed boundary value problem (SPBVP) in the transformed coordinate is less stiff within the boundary layer. An initial value problem for a new dependent variable can be derived easily through the variable transformation. While the zero initial values are given, an unknown terminal value of the new variable at the right end is determined iteratively. We propose the modifications of the asymptotic solution and the uniform approximate solution of the SPBVP; hence, the modified analytic solutions can exactly satisfy both the boundary conditions at two ends. Some examples confirm that the novel methods can achieve better analytic and numerical solutions of the nonlinear SPBVP.

Keywords: Nonlinear singularly perturbed boundary value problem; Initial value problem method; Iterative method; Modified asymptotic solution (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:193:y:2022:i:c:p:139-152

DOI: 10.1016/j.matcom.2021.10.005

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