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Ismail, Hassan N. A.; Abd Rabboh, Aziza A.

A restrictive Padé approximation for the solution of the generalized Fisher and Burger-Fisher equations. (English) Zbl 1050.65077

Appl. Math. Comput. 154, No. 1, 203-210 (2004).
Summary: Solving the generalized Fisher and Burger-Fisher equations by the finite difference technique yields a difficult system of nonlinear equations. In this paper linearization and restrictive Padé approximation is considered. It yields more accurate and faster results. Also the stability analysis is discussed. Numerical results are treated.

Cited in 27 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Burger-Fisher equations; finite difference; Padé approximation; stability; numerical results
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\textit{H. N. A. Ismail} and \textit{A. A. Abd Rabboh}, Appl. Math. Comput. 154, No. 1, 203--210 (2004; Zbl 1050.65077)
Full Text: DOI

References:

[1] Ismail, H. N.A.; Elbarbary, E. M.E., Restrictive Padé approximation and partial differential equation, Int. J. Comput. Math., 66, 343-351 (1998) · Zbl 0894.65039
[2] Ismail, H. N.A.; Elbarbary, E. M.E., Highly accurate method for the convection-diffusion equation, Int. J. Comput. Math., 72, 271-280 (1999) · Zbl 0943.65096
[3] Ismail, H. N.A.; Elbarbary, E. M.E.; Hassan, A. Y., Highly accurate method for solving initial boundary value problem for first order hyperbolic differential equation, Int. J. Comput. Math., 77, 251-261 (2000) · Zbl 1001.65099
[4] Ismail, H. N.A.; Hassan, A. Y., Restrictive Padé approximation for solving first order hyperbolic partial differential equations, J. Inst. Math. Comput. Sci., India, 11, 1, 63-71 (2000)
[5] Ismail, H. N.A.; Hassan, A. Y., Restrictive Padé approximation for solving first order hyperbolic partial differential equation in two space dimensions, J. Inst. Math. Comput. Sci., India, 11, 2, 159-166 (2000)
[6] Ismail, H. N.A.; Elbarbary, E. M.E., Restrictive Taylor expansion and parabolic partial differential equations, Int. J. Comput. Math., 78, 73-82 (2001) · Zbl 0987.65076
[7] Ismail, H. N.A.; Elbeetar, A. A., Restrictive Padé approximation for the solution of singularity perturbed parabolic PDE, J. Inst. Math. Comput. Sci., India, 12, 2, 153-161 (2001)
[8] Ismail, H. N.A.; Elbeetar, A. A., Restrictive Padé approximation for the solution of Schrodinger equation, Int. J. Comput. Math., 79, 5, 603-613 (2002) · Zbl 0999.65087
[9] Wang, X. Y.; Shu, Z. S.; Lu, Y. K., Solitary wave solution of the generalized Burger-Huxly equation, J. Phys. A: Math. Gen., 23, 271-274 (1990) · Zbl 0708.35079
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