A numerical solution for non-classical parabolic problem based on Chebyshev spectral collocation method

Applied Mathematics and Computation

Volumn 190, Issue 1, 2007, Pages 179-185

  Golbabai, A ^a   Javidi, M ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Chebyshev polynomials; Local interpolating functions; Non classical conditions; Parabolic problem

Indexed keywords

CHEBYSHEV APPROXIMATION; COMPUTATIONAL EFFICIENCY; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

LOCAL INTERPOLATING FUNCTIONS; NON-CLASSICAL CONDITIONS; PARABOLIC PROBLEMS;

POLYNOMIALS;

EID: 34249878761     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.01.033     Document Type: Article

References (26)

1. Ang W.T. A boundary integral equation method for the two dimensional diffusion equation subject to a nonlocal conditions. Eng. Anal. Bound Elem. 25 (2001) 1-6
2. Ang W.T. A method of solution for the one-dimensional heat equation subject to nonlocal conditions. Southest Asian Bull. Math. 26 (2002) 185-191
3. Dehghan M. Numerical solution of a parabolic equation with non-local boundary specification. Appl. Math. Comput. 145 (2003) 185-194
4. Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral equation for the wave equation. Numer. Meth. Part. Differ. Eq. 21 (2005) 24-40
5. Dehghan M. Numerical solution of a parabolic equation subject to specification of energy. Appl. Math. Comput. 149 (2004) 31-45
6. Dehghan M. Efficient techniques for the second order parabolic equation subject to nonlocal specifications. Appl. Numer. Math. 52 (2005) 39-62
7. Cannon J.R., Lin Y., and Wang S. An implicit finite difference scheme for the diffusion equation subject to mass specificaion. Int. J. Eng. Sci. 28 (1990) 573-578
8. Cannon J.R., and Matheson A.L. A numerical procedure for diffusion subject to the specification of mass. Int. J. Eng. Sci. 31 (1993) 347-355
9. Cannon J.R., and van der Hoek J. An implicit finite difference scheme for the diffusion equation subject specification of mass in a portion of the domain. In: Noye J. (Ed). Numerical Solutions of Partial Differential Equations (1982), North-Holland Publishing, Amesterdam 527-539
10. Liu Y. Numerical solution of heat equation with nonlocal boundary conditions. J. Comput. Appl. Math. 110 (1999) 115-127
11. wang S., and Lin Y. A numerical method for the diffusion equation with nonlocal boundary specifications. Int. J. Eng. Sci. 28 3-4 (1990) 353-363
12. Dehghan M. On the numerical solution of the diffusion equation with a nonlocal boundary condition. Math. Problem. Eng. 2 (2003) 81-92
13. Ang W.T. Numerical solution of a non-classical parabolic problem: an integro-differential approach. Appl. Math. Comput. 175 2 (2006) 969-979
14. Baltensperger R., and Berrut J.P. The errors in calculating the pseudospectral differentiation matrices for Chebyshev-Gauss-Lobatto point. Comput. Math. Appl. 37 (1999) 41-48
15. Baltensperger R., and Trummer M.R. Spectral differencing with a twist. SIAM J. Sci. Comput. 24 5 (2003) 1465-1487
16. Boyd J.P. Chebyshev and Fourier spectral methods. Lecture Notes in Engineering vol. 49 (1989), Springer-Verlag, Berlin
17. Canuto C., Quarteroni A., Hussaini M.Y., and Zang T. Spectral Method in Fluided Mechanics (1988), Springer-Verlag, New York
18. Don W.S., and Solomonoff A. Accuracy and speed in computing the Chebyshev collocation derivative. SIAM J. Sci. Comput. 16 4 (1995) 1253-1268
19. Trefethen L.N. Spectral Methods in MATLAB (2000), SIAM, Philadelphia
20. Darvishi M.T. Preconditioning and domain decomposition scheme to solve PDEs. Int. J. Pure Appl. Math. 15 4 (2004) 419-439
21. Fornberg B. Generation of finite difference formulas on arbitarily spaced grids. Math. Comput. 51 (1988) 699-706
22. Weideman J.A.C., and Reddy S.C. A MATLAB differentiation matrix suite. Trans. Math. Software 26 (2000) 465-519
23. Welfert B.D. Generation of pseudospectral differentiation matrices, I. SIAM J. Numer. Anal. 34 (1977) 1640-1657
24. Bayliss A., Class A., and Matkowsky B.J. Roundoff error in computing derivatives using the Chebyshev differentiation matrix. J. Comput. Phys. 116 (1995) 380-383
25. Solomonoff A., and Turkel E. Global properties of pseudospectral methods. J. Comput. Phys. 81 (1989) 239-276
26. Tal-Ezer H. Spectral methods in time for hyperbolic equations. SIAM J. Numer. Anal. 23 1 (1986) 11-26