References
- Fisher , RA . 1937 . The wave of advance of advantageous genes . Ann. Eugenics , 7 : 353 – 369 .
- Canosa , J . 1973 . On a nonlinear diffusion equation describing population growth . IBM J. Res. Dev. , 17 : 307 – 313 .
- Kaya , D and El-Sayed , SM . 2004 . A numerical simulation and explicit solutions of the generalized Burger-Fisher equation . Appl. Math. Comput. , 152 : 403 – 413 .
- Ismail , HNA and Rabboh , AAA . 2004 . Arestrictive Padé approximation for the solution of the generalized Fisher and Burger-Fisher equation . Appl. Math. Comput. , 154 : 203 – 210 .
- Ismail , HNA , Raslan , K and Rabboh , AAA . 2004 . Adomian decomposition method for Burgers' Huxley and Burgers'-Fisher equations . Appl. Math. Comput. , 159 : 291 – 301 .
- Wazwaz , AM . 2005 . The tanh method for generalized forms of nonlinear heat conduction and Burgers'-Fisher equations . Appl. Math. Comput. , 169 : 321 – 338 .
- Chen , H and Zhang , H . 2004 . New multiple soliton solutions to the general Burgers'-Fisher equation and the Kuramoto-Sivashinsky equation . Chaos Soliton Fractals , 19 : 71 – 76 .
- El-Wakil , SA and Abdou , MA . 2007 . Modified extended tanh-function method for solving nonlinear partial differential equation . Chaos Soliton Fractals , 31 : 1256 – 1264 .
- Wazwaz , AM . 2007 . The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations . Appl. Math. Comput. , 188 : 1467 – 1475 .
- Moghimi , M and Hejazi , FSA . 2007 . Variational iteration method for solving generalized Burger-Fisher and Burger equations . Chaos Soliton Fractals , 33 : 1756 – 1761 .
- Fahmy , H . 2008 . Travelling wave solutions for some time-delayed equations through factorizations . Chaos Soliton Fractals , 38 : 1209 – 1216 .
- Javidi , M . 2006 . Spectral collocation method for the solution of the generalized Burger-Fisher equation . Appl. Math. Comput. , 174 : 345 – 352 .
- Golbabai , A and Javidi , M . 2009 . A spectral domain decomposition approach for the generalized Burgers'-Fisher equation . Chaos Soliton Fractals , 39 : 385 – 392 .
- Wazzan , L . 2009 . A modified tanh–coth method for solving the general Burgers-Fisher and the Kuramoto-Sivashinsky equations . Commun. Nonlinear Sci. Numer. Simulat. , 14 : 2642 – 2652 .
- Wu , G-C . 2009 . Uniformly constructing soliton solutions and periodic solutions to Burgers'-Fisher equation . Comput. Math. Appl. , 58 : 2355 – 2357 .
- Rashidi , MM , Ganji , DD and Dinarvand , S . 2009 . Explicit analytical solutions of the generalized Burger and BurgerFisher equations by homotopy perturbation method . Numer. Methods Partial Differ. Eqns , 25-2 : 409 – 417 .
- Xu , Z-H and Xian , DQ . 2010 . Application of Exp-function method to generalized Burgers'-Fisher equation . Acta Math. Appl. Sinica (English Series) , 26-4 : 669 – 676 .
- Tatari , M , Sepehrian , B and Alibakhshi , M . 2011 . New implementation of radial basis functions for solving Burgers'-Fisher equation . Numer. Methods Partial Differ. Eqns , 27 DOI: 10.1002/num.20617
- Hirsh , RS . 1975 . Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique . J. Comput. Phys. , 19 : 90 – 109 .
- Ciment , M , Leventhal , SH and Weinberg , BC . 1978 . The operator compact implicit method for parabolic equations . J. Comput. Phys. , 28 : 135 – 166 .
- Rigal , A . 1994 . High order difference schemes for unsteady one-dimensional diffusion-convection problems . J. Comput. Phys. , 114 : 59 – 76 .
- Chu , PC and Fan , C . 1998 . A three-point combined compact difference scheme . J. Comput. Phys. , 140 : 370 – 399 .
- Karaa , S and Zhang , J . 2004 . High order ADI method for solving unsteady convection-diffusion problems . J. Comput. Phys. , 198 : 1 – 9 .
- Li , J . 2005 . High-order finite difference schemes for differential equations containing higher derivatives . Appl. Math. and Comput. , 171 : 1157 – 1176 .
- Liao , W . 2008 . An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation . Appl. Math. Comput. , 206 : 755 – 764 .
- Bratsos , AG and Petrakis , LA . 2011 . An explicit numerical scheme for the modified Burgers' equation . Commun. Numer. Methods Eng. , 27 : 232 – 237 .
- Sari , M and Gürarslan , G . 2009 . A sixth-order compact finite difference scheme to the numerical solutions of Burgers' equation . Appl. Math. Comput. , 208 : 475 – 483 .
- Sari , M . 2009 . Solution of the porous media equation by a compact finite difference method . Math. Probl. Eng. , 2009
- Sari , M , Gürarslan , G and Dag , I . 2010 . A compact finite difference method for the solution of the generalized Burgers'-Fisher equation . Numer. Methods Partial Differ. Eqns , 26 : 125 – 134 .
- Sari , M , Gürarslan , G and Zeytinoğlu , A . 2011 . High-order finite difference schemes for the solution of the generalized Burgers'-Fisher equation . Commun. Numer. Methods Eng. , 27 DOI: 10.1002/cnm.1360
- Zhu , C-G and Wang , R-H . 2009 . Numerical solution of Burgers' equation by cubic B-spline quasi-interpolation . Appl. Math. Comput. , 208 : 260 – 272 .
- Zhu , C-G and Kang , W-S . 2010 . Numerical solution of Burgers'-Fisher equation by cubic B-spline quasi-interpolation . Appl. Math. Comput. , 216 : 2679 – 2686 .
- Griewank , A and El-Danaf , TS . 2009 . Efficient accurate numerical treatment of the modified Burgers' equation . Appl. Anal. , 88 ( 1 ) : 75 – 87 .
- Rashidinia , J and Mohammadi , R . 2010 . Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation . Comput. Phys. Commun. , 181 : 78 – 91 .
- Rashidinia , J and Mohammadi , R . 2011 . Tension spline solution of nonlinear sine-Gordon equation . Numer. Algorithms , 56 : 129 – 142 .
- Samarskii , AA and Andreev , VB . 1976 . Difference Methods for Elliptic Equations , Moscow : Nauka .