On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation
We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergenc...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/763160 |
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| author | H. S. Mamba M. Khumalo |
| author_facet | H. S. Mamba M. Khumalo |
| author_sort | H. S. Mamba |
| collection | DOAJ |
| description | We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results. |
| format | Article |
| id | doaj-art-acef612fcf7d4db0a22c168cfe3219e4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-acef612fcf7d4db0a22c168cfe3219e42025-02-03T05:50:28ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/763160763160On the Analysis of Numerical Methods for Nonstandard Volterra Integral EquationH. S. Mamba0M. Khumalo1Department of Pure and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South AfricaDepartment of Pure and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South AfricaWe consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.http://dx.doi.org/10.1155/2014/763160 |
| spellingShingle | H. S. Mamba M. Khumalo On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation Abstract and Applied Analysis |
| title | On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation |
| title_full | On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation |
| title_fullStr | On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation |
| title_full_unstemmed | On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation |
| title_short | On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation |
| title_sort | on the analysis of numerical methods for nonstandard volterra integral equation |
| url | http://dx.doi.org/10.1155/2014/763160 |
| work_keys_str_mv | AT hsmamba ontheanalysisofnumericalmethodsfornonstandardvolterraintegralequation AT mkhumalo ontheanalysisofnumericalmethodsfornonstandardvolterraintegralequation |