Fully discrete Tau solution for some types of non-local heat transport equations

References

• Saadatmandi A, Razzaghi M. A tau method approach for the diffusion equation with nonlocal boundary conditions. Int J Comput Math. 2004;81:1427–1432.
   Web of Science ®Google Scholar
• Dehghan M. Numerical solution of a parabolic equation with non-local boundary specifications. Appl Math Comput. 2003;145:185–194.
   Web of Science ®Google Scholar
• Tatari M, Dehghan M. On the solution of the non-local parabolic partial differential equations via radial basis functions. Appl Math Model. 2009;33:1729–1738.
   Web of Science ®Google Scholar
• Avalishvili G, Avalishvili M, Gordeziani D. On integral nonlocal boundary value problems for some partial differential equations. Bull Georegian Nat Acad Sci. 2011;5:31–37.
   Google Scholar
• Berikelashvili G, Khomeriki N. On the convergence of difference schemes for one nonlocal boundary-value problem. Lithuanian Math J. 2012;52:353–362.
   Web of Science ®Google Scholar
• Martin-Vaquero J, Queiruga-Dios A, Encinas A. Numerical algorithms for diffusion-reaction problems with non-classical conditions. Appl Math Comput. 2012;218:5487–5495.
   Web of Science ®Google Scholar
• Martin-Vaquero J, Wade BA. On efficient numerical methods for an initial-boundary value problem with nonlocal boundary conditions. Appl Math Model. 2012;36:3411–3418.
   Web of Science ®Google Scholar
• Shen J, Tang T. Spectral and high-order methods with applications. Beijing: Science Press; 2006.
   Google Scholar
• Dehghan M. Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Appl Num Math. 2005;25:39–62.
   Google Scholar
• Dehghan M. A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Numer Meth Part D E. 2006;22:220–257.
   Web of Science ®Google Scholar
• Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Soliton Fract. 2007;32:661–675.
   Web of Science ®Google Scholar
• Lanczos C. Trigonometric interpolation of empirical and analytical functions. J Math Phys. 1938;17:123–199.
   Google Scholar
• Shaban M, Kazem S, Rad JA. A modification of the homotopy analysis method based on Chebyshev operational matrices. Math Comput Model. 2013;57:1227–1239.
   Google Scholar
• Tajvidi T, Razzaghi M, Dehghan M. Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate. Chaos Soliton Fract. 2008;35:59–66.
   Web of Science ®Google Scholar
• Razzaghi M, Oppenheimer S, Ahmad F. Tau method approximation for radiative transfer problems in a slab medium. JQSRT. 2002;72:439–447.
   Web of Science ®Google Scholar
• Kazem S, Shaban M, Rad JA. Solution of Coupled Burger’s equation based on operational matrices of d-dimensional orthogonal functions. Z Naturforsch. 2012;67a:267–274.
   Google Scholar
• Eslahchi M, Dehghan M. Application of taylor series in obtaining the orthogonal operational matrix. Comput Math Appl. 2011;61:2596–2604.
   Web of Science ®Google Scholar
• Ionkin N. Stability of a problem in heat transfer theory with a non-classical boundary condition. Differ Equ. 1980;15:911–914.
   Google Scholar
• Makarov V, Kulyev D. Solution of a boundary value problem for a quasi-linear parabolic equation with nonclassical boundary conditions. Differ Equ. 1985;21:296–305.
   Web of Science ®Google Scholar
• Cannon J, Matheson A. A numerical procedure for diffusion subject to the specification of mass. Int J Eng Sci. 1993;31:347–355.
   Web of Science ®Google Scholar
• Cannon J, van der Hoek J. Implicit finite difference scheme for the diffusion of mass in porous media. Numerical solution of partial differential equations. Amsterdam: North Holland; 1982. p. 527–539.
   Google Scholar
• Ang W. A method of solution for the heat equation subject to a nonlocal condition. SEA Bull Math. 2002;26:197–203.
   Google Scholar
• Lihua M, Hong D. The solution of a parabolic differential equation with non-local boundary conditions in the reproducing kernel space. Appl Math Comput. 2008;202:708–714.
   Web of Science ®Google Scholar
• Martin-Vaquero J, Vigo-Aguiar J. A note on efficient techniques for the second-order parabolic equation subject to non-local conditions. Appl Numer Math. 2011;59:1258–1264.
   Web of Science ®Google Scholar
• Yousefi S, Behroozifar M, Dehghan M. The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass. J Comput Appl Math. 2011;235:5272–5283.
   Web of Science ®Google Scholar
• Boyd J. Chebyshev and Fourier spectral methods. New York (NY): Springer-Verlag; 2001.
   Google Scholar
• Rudin W. Real and complex analysis. New York (NY): Tata McGraw-Hill Education; 1987.
   Google Scholar
• Watson GA. Approximation theory and numerical methods. New York (NY): John Wiley & Sons; 1980.
   Google Scholar
• Gautschi W. Numerical analysis. Springer Science & Business Media; 2011.
   Google Scholar
• Saadatmandi A, Dehghan M. A tau approach for solution of the space fractional diffusion equation. Comput Math Appl. 2011;62(3):1135–1142.
   Web of Science ®Google Scholar
• Doha EH, Bhrawy AH, Ezz-Eldien SS. Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Appl Math Modell. 2011;35(12):5662–5672.
   Web of Science ®Google Scholar
• Saadatmandi A, Dehghan M. A new operational matrix for solving fractional-order differential equations. Comput Math Appl. 2010;59:1326–1336.
   Web of Science ®Google Scholar
• Doha EH, Bhrawy AH, Ezz-Eldien SS. Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method. Cent Eur J Phys. 2013;11:1494–1503.
   Google Scholar
• Doha EH, Bhrawy AH, Ezz-Eldien SS. A new Jacobi operational matrix: An application for solving fractional differential equations. Appl Math Modell. 2012;36:4931–4943.
   Web of Science ®Google Scholar
• Tatari M, Dehghan M. On the solution of the non-local parabolic partial differential equations via radial basis functions. Appl Math Modell. 2009;33:1729–1738.
   Web of Science ®Google Scholar