A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations
A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating su...
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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/10.1155/2014/975985 |
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| _version_ | 1832557136579657728 |
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| author | Xiaomin Wang |
| author_facet | Xiaomin Wang |
| author_sort | Xiaomin Wang |
| collection | DOAJ |
| description | A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating such a modified wavelet approximation scheme into the conventional Galerkin method, the nonsingular property of the connection coefficients significantly reduces the computational complexity and achieves high precision in a very simple way. Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. At last, numerical simulations are performed to show the efficiency of the method proposed. |
| format | Article |
| id | doaj-art-f200c1be7b0d4915b49512fa8d915ed0 |
| 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-f200c1be7b0d4915b49512fa8d915ed02025-02-03T05:43:33ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/975985975985A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral EquationsXiaomin Wang0School of Engineering, Huazhong Agricultural University, Wuhan, Hubei 430070, ChinaA new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating such a modified wavelet approximation scheme into the conventional Galerkin method, the nonsingular property of the connection coefficients significantly reduces the computational complexity and achieves high precision in a very simple way. Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. At last, numerical simulations are performed to show the efficiency of the method proposed.http://dx.doi.org/10.1155/2014/975985 |
| spellingShingle | Xiaomin Wang A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations Abstract and Applied Analysis |
| title | A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations |
| title_full | A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations |
| title_fullStr | A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations |
| title_full_unstemmed | A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations |
| title_short | A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations |
| title_sort | new wavelet method for solving a class of nonlinear volterra fredholm integral equations |
| url | http://dx.doi.org/10.1155/2014/975985 |
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