Numerical solution of time-dependent diffusion equations with nonlocal boundary conditions via a fast matrix approach | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 24, Issue 1, 2016, Pages 86-91 PDF (1.04 M) | ||
| DOI: 10.21608/joems.2016.386811 | ||
| Authors | ||
| Emran Tohidi1; Faezeh Toutounian2 | ||
| 1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2The Center of Excellence on Modelling and Control Systems, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| Abstract | ||
| This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs) subject to nonlocal boundary integral conditions. We first impose the initial and boundary conditions to the main problems and then reach to the associated integro-PDEs. By using operational matrices and also the completeness of the monomials basis, the obtained integro-PDEs will be reduced to the generalized Sylvester equations. For solving these algebraic systems, we apply a famous technique in Krylov subspace iterative methods. A numerical example is considered to show the efficiency of the proposed idea. | ||
| Keywords | ||
| One-dimensional parabolic equation; Nonlocal boundary conditions; Taylor approximation; Operational matrices; Krylov subspace iterative methods; Restarted GMRES | ||
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