http://scholars.ntou.edu.tw/handle/123456789/15024
Title: | Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions | Authors: | Chein-Shan Liu Jiang-Ren Chang |
Keywords: | boundary shape functions;collocation method;iterative method;nonlinear singularly perturbed boundary value problem;Robin boundary conditions | Issue Date: | 27-Jun-2020 | Journal Volume: | 21 | Journal Issue: | 7-8 | Start page/Pages: | 797–806 | Source: | International Journal of Nonlinear Sciences and Numerical Simulation | Abstract: | International Journal of Nonlinear Sciences and Numerical Simulation | Volume 21: Issue 7-8 Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions Chein-Shan LiuORCID iD: https://orcid.org/0000-0001-6366-3539 and Jiang-Ren Chang DOI: https://doi.org/10.1515/ijnsns-2019-0209 | Published online: 27 Jul 2020 ABSTRACT FULL TEXT REFERENCES RECOMMENDATIONS Abstract For a second-order nonlinear singularly perturbed boundary value problem (SPBVP), we develop two novel algorithms to find the solution, which automatically satisfies the Robin boundary conditions. For the highly singular nonlinear SPBVP the Robin boundary functions are hard to be fulfilled exactly. In the paper we first introduce the new idea of boundary shape function (BSF), whose existence is proven and it can automatically satisfy the Robin boundary conditions. In the BSF, there exists a free function, which leaves us a chance to develop new algorithms by adopting two different roles of the free function. In the first type algorithm we let the free functions be the exponential type bases endowed with fractional powers, which not only satisfy the Robin boundary conditions automatically, but also can capture the singular behavior to find accurate numerical solution by a simple collocation technique. In the second type algorithm we let the BSF be solution and the free function be another variable, such that we can transform the boundary value problem to an initial value problem (IVP) for the new variable, which can quickly find accurate solution for the nonlinear SPBVP through a few iterations. |
URI: | http://scholars.ntou.edu.tw/handle/123456789/15024 | DOI: | 10.1515/ijnsns-2019-0209 |
Appears in Collections: | 系統工程暨造船學系 |
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