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Djaokamla, Temga; Ndeuzoumbet, Siniki; Sylvain, Koumla

Pseudo-spectral and forward Euler scheme methods for solving nonlinear evolution partial differential equation in 2D-space. (English) Zbl 07480290

Int. J. Numer. Methods Appl. 19, No. 1, 29-41 (2020).

MSC:

47J35 Nonlinear evolution equations
35M13 Initial-boundary value problems for PDEs of mixed type
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
80M22 Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer

Keywords:

pseudo-spectral method; finite difference; Lagrange interpolation; EDPs evolution
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References:

[1] M. Abutheraa and D. Lester, Computable function representation using effective Chebyshev polynomial, 4th CMSE (2007), 103-110.
[2] Alberto Mardegan, Alvise Sommariva, Marco Vianello and Renato Zanovello, Adaptative bivariate Chebyshev approximation and efficient evaluation of integral operators, Wiley-VCH, Weinheim, 2003. · Zbl 1060.65689
[3] N. K. Basu, On double Chebyshev series approximation, SIAM J. Numer. Anal. 10 (1973), 496-505. · Zbl 0254.41011
[4] J.-P. Demailly, Analyse numrique et equations differentielles, EDP Sciences (Collection Grenoble), 2016. · Zbl 1362.65001
[5] M. Druon, Modlisation du mouvement par polynmes orthogonaux-application l’tude d’coulements uides, Ph.D. Thesis, Universit de Poitier, 2009.
[6] B. Fornberg, A Practical Guide to Pseudo-spectral Methods, Cambridge University Press, Cambridge, 1998. · Zbl 0912.65091
[7] D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods -Theory and Applications, SIAM, Philadelphia, 1977. · Zbl 0412.65058
[8] D. Kincaid and W. Cheney, Numerical Analysis, Mathematics of Scientific Computing, Brooks/Cole, 2002. · Zbl 1222.65001
[9] V. M. Magagula, S. S. Motsa and P. Sibanda, A multi-domain bivariate pseudo-spectral method for evolution equations, Int. J. Comput. Methods 14(4) (2017), 1750041, 27 pp. · Zbl 1404.65198
[10] J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, CRC Press, 2003. · Zbl 1015.33001
[11] R. Nawaz, H. Ullah, S. Islam and M. Idrees, Application of optimal homotopy asymptotic method to Burger equations, J. Appl. Math. 2013, Art. ID 387478, 8 pp. · Zbl 1271.35063
[12] Robert A. Adams, Sobolev Spaces, Academic Press, Columbia University, New York, 1975. · Zbl 0314.46030
[13] J. Sherratt, On the transition from initial data to travelling waves in the Fisher-KPP equation, Dynam. Stability Systems 13 (1998), 167-174. · Zbl 0912.35084
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