Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
| Autor: | Jiang-Ren Chang, Chein-Shan Liu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Mathematical analysis Computational Mechanics General Physics and Astronomy Statistical and Nonlinear Physics Fluid mechanics 01 natural sciences Robin boundary condition 010305 fluids & plasmas 010101 applied mathematics Nonlinear system Mechanics of Materials Modeling and Simulation 0103 physical sciences 0101 mathematics Boundary shape Engineering (miscellaneous) Mathematics |
| Zdroj: | International Journal of Nonlinear Sciences and Numerical Simulation. 21:797-806 |
| ISSN: | 2191-0294 1565-1339 |
| DOI: | 10.1515/ijnsns-2019-0209 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|