Existence and approximation of solution for a nonlinear second-order three-point boundary value problem
| Autor: | Qiong-Ao Huang, Han-Mei Wei, Xian-Ci Zhong |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Mathematical analysis Exponential integrator 01 natural sciences 010101 applied mathematics Examples of differential equations Nonlinear system Collocation method Initial value problem Boundary value problem 0101 mathematics C0-semigroup Analysis Numerical partial differential equations Mathematics |
| Zdroj: | Boundary Value Problems. 2016(1) |
| ISSN: | 1687-2770 |
| DOI: | 10.1186/s13661-016-0678-4 |
| Popis: | A nonlinear second-order ordinary differential equation with four cases of three-point boundary value conditions is studied by investigating the existence and approximation of solutions. First, the integration method is proposed to transform the considered boundary value problems into Hammerstein integral equations. Second, the existence of solutions for the obtained Hammerstein integral equations is analyzed by using the Schauder fixed point theorem. The contraction mapping theorem in Banach spaces is further used to address the uniqueness of solutions. Third, the approximate solution of Hammerstein integral equations is constructed by using a new numerical method, and its convergence and error estimate are analyzed. Finally, some numerical examples are addressed to verify the given theorems and methods. |
| Databáze: | OpenAIRE |
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