Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes
Of concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is redu...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/10957 |
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| author | G. E. Okecha |
| author_facet | G. E. Okecha |
| author_sort | G. E. Okecha |
| collection | DOAJ |
| description | Of concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. A few numerical results are given to illustrate and validate the power of the method developed. Our method is more accurate than some earlier methods developed to tackle this problem. |
| format | Article |
| id | doaj-art-edcb168234784a41a4d2b29cfa715b62 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-edcb168234784a41a4d2b29cfa715b622025-02-03T01:25:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/1095710957Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation NodesG. E. Okecha0Department of Mathematics, (Pure and Applied), University of Fort Hare, Alice 5700, South AfricaOf concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. A few numerical results are given to illustrate and validate the power of the method developed. Our method is more accurate than some earlier methods developed to tackle this problem.http://dx.doi.org/10.1155/2007/10957 |
| spellingShingle | G. E. Okecha Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes International Journal of Mathematics and Mathematical Sciences |
| title | Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes |
| title_full | Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes |
| title_fullStr | Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes |
| title_full_unstemmed | Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes |
| title_short | Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes |
| title_sort | solution of cauchy type singular integral equations of the first kind with zeros of jacobi polynomials as interpolation nodes |
| url | http://dx.doi.org/10.1155/2007/10957 |
| work_keys_str_mv | AT geokecha solutionofcauchytypesingularintegralequationsofthefirstkindwithzerosofjacobipolynomialsasinterpolationnodes |