Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-08-31
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Cai, Haotao. 2017. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels. Journal of Function Spaces،Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1176473
Modern Language Association (MLA)
Cai, Haotao. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels. Journal of Function Spaces No. 2017 (2017), pp.1-11.
https://search.emarefa.net/detail/BIM-1176473
American Medical Association (AMA)
Cai, Haotao. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels. Journal of Function Spaces. 2017. Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1176473
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176473