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Space-time Muntz spectral collocation approach for parabolic Volterra integro-differential equations with a singular kernel | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 14، شماره 3، خرداد 2023، صفحه 153-162 اصل مقاله (11.92 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25948.3168 | ||
| نویسندگان | ||
| Bahareh Sadeghi؛ Mohammad Maleki* ؛ Homa Almasieh | ||
| Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran | ||
| تاریخ دریافت: 26 دی 1400، تاریخ پذیرش: 22 اسفند 1400 | ||
| چکیده | ||
| We consider a type of Volterra integro-differential equations of the parabolic type that arise naturally in the study of heat flow in materials with memory. We present a simple and accurate numerical method for problems with a weakly singular kernel subject to an initial condition and given boundary conditions. In this method, both the space and time discretizations are based on the Muntz-Legendre collocation method that converts the problem to a system of algebraic equations. For numerical stability purposes, the Muntz-Legendre polynomials and their partial derivatives are stated in terms of Jacobi polynomials. Moreover, to deal with the weakly singular integral term of the problem, two efficient schemes based on the integration by parts and nonclassical Gaussian quadrature are derived. Comparisons between the two proposed schemes and other methods in the literature are made to demonstrate the efficiency, convergence and superiority of our method in the space and time directions. | ||
| کلیدواژهها | ||
| Parabolic integro-differential equation؛ Heat flow؛ Singular kernel؛ Muntz-Legendre collocation؛ Nonclassical Gauss quadrature formulas | ||
| مراجع | ||
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