Spectral method for the diffusion equation with a source term | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 110، دوره 13، شماره 2، مهر 2022، صفحه 1343-1355 اصل مقاله (520.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.19444.2082 | ||
| نویسندگان | ||
| Ahcene Lateli* 1؛ Amor Boutaghou2؛ Tayeb Hamaizia1 | ||
| 1Institute of Mathematics, Department of Mathematics, University of Mentouri, Constantine 25000, Algeria | ||
| 2Institute of Mathematics, Department of Mathematics, University of Dr. Yahia Fares, Medea, Algeria | ||
| چکیده | ||
| The aim of this paper is to investigate the Legendre spectral method for solving the diffusion equation with a source term and mixed initial-boundary value problem in a finite rectangle $\Omega _{2}$, we use some techniques to convert the problem to a system of ordinary differential equations and by an analysis matrical we find a general term defines all ordinary differential equations of this system, we solve this general term we get the desired approximate solution, we also present the error estimate. | ||
| کلیدواژهها | ||
| Diffusion Equation؛ Spectral method؛ Orthogonal polynomials؛ Quadrature formula؛ Orthogonal matrix؛ Eigenvalues؛ error estimate | ||
| مراجع | ||
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