Jacobi spectral solution for integral algebraic equations of index-2

• Published in: Applied numerical mathematics Vol. 61; no. 1; pp. 131 - 148
• Main Authors: Hadizadeh, M., Ghoreishi, F., Pishbin, S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 2011; Elsevier
• Subjects: Error analysis; Exact sciences and technology; Index of IAEs; Integral algebraic equations; Integral equations; Jacobi collocation method; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Operator theory; Sciences and techniques of general use; Sequences, series, summability; System of Volterra equations; Index of IAEs; Error analysis; System of Volterra equations; Integral algebraic equations; Jacobi collocation method; Transcendental equation; Multiplication; Jacobi method; Convergence acceleration; Jacobi matrix; Explicit equation; Equation system; Non linear equation; Kernel function; Numerical analysis; Applied mathematics; Smooth function; Algebraic equation; Convergence rate; Matrix method; Integral equation; Collocation method
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2010.08.009

This paper is concerned with obtaining the approximate solution of a class of semi-explicit Integral Algebraic Equations ( IAEs) of index-2. A Jacobi collocation method including the matrix–vector multiplication representation is proposed for the IAEs of index-2. A rigorous analysis of error bound in weighted L 2 norm is also provided which theoretically justifies the spectral rate of convergence while the kernels and the source functions are sufficiently smooth. Results of several numerical experiments are presented which support the theoretical results.