An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition
| Autor: | Kourosh Parand, Saeid Abbasbandy, Babak Azarnavid |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Iterative method Applied Mathematics 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Nonlinear boundary conditions Nonlinear system Kernel method Modeling and Simulation Kernel (statistics) Applied mathematics Boundary value problem Uniqueness 0101 mathematics Reproducing kernel Hilbert space Mathematics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 59:544-552 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2017.12.002 |
| Popis: | This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect