Dehghan, Mehdi; Shamsi, M. Numerical solution of two-dimensional parabolic equation subject to nonstandard boundary specifications using the pseudospectral Legendre method. (English) Zbl 1108.65101 Numer. Methods Partial Differ. Equations 22, No. 6, 1255-1266 (2006). Summary: The problem of solving a two-dimensional parabolic equation subject to a given initial condition and nonlocal boundary specifications is considered. A technique based on the pseudospectral Legendre method is proposed for the numerical solution of the studied problem. Several examples are given and numerical results are shown to demonstrate the efficiently of the newly proposed method. Cited in 15 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation Keywords:two-dimensional parabolic partial differential equation; nonlocal boundary conditions; spectral method; specification of mass; numerical results PDF BibTeX XML Cite \textit{M. Dehghan} and \textit{M. Shamsi}, Numer. Methods Partial Differ. Equations 22, No. 6, 1255--1266 (2006; Zbl 1108.65101) Full Text: DOI References: [1] Capasso, Quart Appl Math 46 pp 431– (1988) [2] Day, Quart Appl Math 41 pp 468– (1983) [3] Cannon, Int J Eng Sci 28 pp 573– (1990) [4] Ang, SEA Bull Math 26 pp 197– (2002) [5] Dehghan, Appl Math Comput 145 pp 185– (2003) [6] Dehghan, Appl Numer Math 52 pp 39– (2005) [7] Ekolin, BIT 31 pp 245– (1991) [8] Dehghan, Appl Math Comput 149 pp 31– (2004) [9] Saadatmandi, Int J Comput Math 81 pp 1427– (2004) [10] Dehghan, Commun Numer Methods Engng 19 pp 1– (2003) [11] Cannon, SIAM J Numer Anal 24 pp 499– (1987) [12] Cannon, J Differential Eqs 79 pp 266– (1989) [13] Day, Quart Appl Math 40 pp 319– (1982) [14] Friedman, Quart Appl Math 44 pp 468– (1986) [15] Kawohl, Quart Appl Math 45 pp 751– (1987) [16] Lin, Int J Math Math Sci 20 pp 147– (1997) [17] Spectral methods in MATLAB, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. · Zbl 0953.68643 · doi:10.1137/1.9780898719598 [18] , , , Spectral methods in fluid dynamics, Springer-Verlag, New York, 1988. · Zbl 0658.76001 · doi:10.1007/978-3-642-84108-8 [19] Wang, Int J Eng Sci 28 pp 543– (1990) [20] Chebyshev and Fourier spectral methods, Dover Publications, Mineola, NY, 2001. · Zbl 0994.65128 [21] Fahroo, J Guid Control Dynam 25 pp 160– (2002) [22] , , Exploiting higher-order derivatives in computational optimal control, presented at the IEEE Mediterranean Conf. Control and Automation, Lisbon, Portugal, July 2002. [23] Dehghan, Numer Methods Partial Differential Equations 21 pp 24– (2005) [24] Dehghan, Appl Math Comput 167 pp 28– (2005) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.