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Spectral collocation method and Darvishi’s preconditionings to solve the generalized Burgers-Huxley equation. (English) Zbl 1221.65261
Summary: A numerical solution of the generalized Burgers-Huxley equation is presented. This is the application of spectral collocation method. To reduce roundoff error in this method we use Darvishi’s preconditionings. The numerical results obtained by this method have been compared with the exact solution. It can be seen that they are in a good agreement with each other, because errors are very small and figures of exact and numerical solutions are very similar.

##### MSC:
 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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##### References:
 [1] Baltensperger, R.; Berrut, J.P., The errors in calculating the pseudospetral differentiation matrices for chebvshev – gauss – lobatto points, Comput math appl, 37, 41-48, (1999) · Zbl 0940.65021 [2] Baltensperger, R.; Trummer, M.R., Spectral differencing with a twist, SIAM J sci comput, 24, 5, 1465-1487, (2003) · Zbl 1034.65016 [3] Bayliss, A.; Class, A.; Matkowsky, B., Roundoff error in computing derivatives using the Chebyshev differentiation matrix, J comput phys, 116, 380-383, (1995) · Zbl 0826.65014 [4] Breuer, K.S.; Everson, R.S., On the errors incurred calculating derivatives using Chebyshev polynomials, J comput phys, 99, 56-67, (1992) · Zbl 0747.65009 [5] Darvishi, M.T.; Ghoreishi, F., Error reduction for higher derivatives of Chebyshev collocation method using preconditioning and domain decomposition, Korean J comput appl math, 6, 2, 421-435, (1999) · Zbl 0931.65051 [6] Darvishi, M.T., Preconditioning and domain decomposition schemes to solve pdes, Int J pure appl math, 1, 4, 419-439, (2004) · Zbl 1127.65324 [7] Don, W.S.; Solomonoff, A., Accuracy and speed in computing the Chebyshev collocation derivative, SIAM J sci comput, 16, 4, 1253-1268, (1995) · Zbl 0840.65010 [8] Don, W.S.; Solomonoff, A., Accuracy enhancement for higher derivatives using Chebyshev collocation and a mapping technique, SIAM J sci comput, 18, 4, 1040-1055, (1997) · Zbl 0906.65019 [9] Estevez, P.G., Non-classical symmetries and the singular modified the burger’s and burger’s – huxley equation, J phys A, 27, 2113-2127, (1994) · Zbl 0838.35114 [10] Gottlieb, D.; Hussaini, M.Y.; Orszag, S.A., Theory and application of spectral methods, (), 1-54 [11] Ismail, H.N.A.; Raslan, K.; Rabboh, A.A.A., Adomian decomposition method for burger’s Huxley and burger’s – fisher equations, Appl math comput, 159, 291-301, (2004) · Zbl 1062.65110 [12] Ralston, A., A first course in numerical analysis, (1965), McGraw-Hill · Zbl 0139.31603 [13] Solomonoff, A.; Turkel, E., Global properties of pseudospectral methods, J comput phys, 81, 239-276, (1989) · Zbl 0668.65091 [14] Tang, T.; Trummer, M.R., Boundary layer resolving pseudospetral methods for singular perturbation problems, SIAM J sci comput phys, 17, 430-438, (1996) · Zbl 0851.65058 [15] Wang, X.Y.; Zhu, Z.S.; Lu, Y.K., Solitary wave solutions of the generalized burger’s – huxley equation, J phys A: math gen, 23, 271-274, (1990) · Zbl 0708.35079
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