Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes | Zendy

G. E. Okecha | Zendy

Open Access

Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes

Author(s) -

G. E. Okecha

Publication year - 2007

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2007/10957

Subject(s) - mathematics , quadrature (astronomy) , interpolation (computer graphics) , algebraic equation , mathematical analysis , type (biology) , singular integral , nyström method , integral equation , nonlinear system , animation , physics , computer graphics (images) , quantum mechanics , computer science , electrical engineering , engineering , ecology , biology

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

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