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A spectral collocation method using orthogonal polynomials for Volterra integro-differential equations of the second kind with discontinuous kernels | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 31 مرداد 1405 اصل مقاله (363.33 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.33777.3102 | ||
| نویسندگان | ||
| Mina Mousavi Kamazani؛ Farshid Mirzaee* | ||
| Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran | ||
| چکیده | ||
| This paper presents a spectral collocation approach using shifted Legendre polynomials on the interval I = [0,T] for solving a class of linear Volterra integro-differential equations with discontinuous kernels. The unknown solution and the kernels are approximated by truncated orthogonal polynomial expansions, and suitable operational matrices for integration, differentiation, and product are constructed. The collocation scheme transforms the original problem into a system of linear algebraic equations for unknown coefficients. An explicit L2-error bound for the proposed approximation is derived under appropriate regularity assumptions. Numerical examples are provided to demonstrate efficiency and accuracy of the method. The method is developed under the assumption that the discontinuity curves are affine functions; extensions to general curves are discussed as a future direction. | ||
| کلیدواژهها | ||
| Volterra integro-differential equations؛ Discontinuous kernels؛ Orthogonal polynomials؛ Spectral collocation method؛ Error analysis | ||
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آمار تعداد مشاهده مقاله: 20 تعداد دریافت فایل اصل مقاله: 13 |
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