Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-J...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/4751357 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549822576459776 |
|---|---|
| author | Haotao Cai |
| author_facet | Haotao Cai |
| author_sort | Haotao Cai |
| collection | DOAJ |
| description | We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-c958d0b3edd844b08255e794d96975b1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c958d0b3edd844b08255e794d96975b12025-02-03T06:08:31ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/47513574751357Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular KernelsHaotao Cai0School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, ChinaWe develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2017/4751357 |
| spellingShingle | Haotao Cai Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels Journal of Function Spaces |
| title | Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels |
| title_full | Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels |
| title_fullStr | Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels |
| title_full_unstemmed | Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels |
| title_short | Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels |
| title_sort | convergence analysis of generalized jacobi galerkin methods for second kind volterra integral equations with weakly singular kernels |
| url | http://dx.doi.org/10.1155/2017/4751357 |
| work_keys_str_mv | AT haotaocai convergenceanalysisofgeneralizedjacobigalerkinmethodsforsecondkindvolterraintegralequationswithweaklysingularkernels |