References
- Mitchell , A. R. and Griffiths , D. F. 1980 . The Finite Difference Method In Partial Equations , New York : John Wiley .
- Adomian , G. 1994 . Solving Frontier Problems of Physics: The Decomposition Method , Boston, MA : Kluwer Academic .
- Parkes , E. J. and Duffy , B. R. 1998 . An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations . Computer Physics Communications , 98 : 288 – 300 .
- Khater , A. H. , Malfiet , W. , Callebaut , D. K. and Kamel , E. S. 2002 . The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations . Chaos, Solitons & Fractals , 14 : 513 – 522 .
- Fan , E. 2000 . Extended tanh-function method and its applications to nonlinear equations . Physics Letters A , 277 : 212 – 218 .
- Fan , E. 2001 . Travelling wave solutions for generalized Hirota–Satsuma coupled KdV systems . Zeitschrift für Naturforschung A , 56 : 312 – 318 .
- Elwakil , S. A. , El-Labany , S. K. , Zahran , M. A. and Sabry , R. 2002 . Modified extended tanh-function method for solving nonlinear partial differential equations . Physics Letters A , 299 : 179 – 188 .
- Gao , Y. T. and Tian , B. 2001 . Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics . Computer Physics Communications , 133 : 158 – 164 .
- Tian , B. and Gao , Y. T. 2002 . Observable solitonic features of the generalized reaction Duffing model . Zeitschrift für Naturforschung A , 57 : 39 – 44 .
- Tang , X.-Y. and Lou , S.-Y. 2002 . Abundant structures of the dispersive long-wave equation in (2+1)-dimensional spaces . Chaos, Solitons & Fractals , 14 : 1451 – 1456 .
- Tang , X. -Y. and Lou , S. -Y. 2002 . Localized excitations in (2+1)-dimensional systems . Physical Review E , 66 : 46601 – 46617 .
- Gardner , L. R.T. and Gardner , G. A. 1990 . Solitary waves of the equal width wave equation . Journal of Computational Physics , 101 : 218 – 223 .
- Zaki , S. I. 2000 . A least-squares finite element scheme for the EW equation . Computer Methods in Applied Mechanics and Engineering , 189 : 587 – 594 .
- Zaki , S. I. 2001 . Solitary Waves Induced by The Boundary Forced EW Equation . Computer Methods in Applied Mechanics and Engineering , 190 : 4881 – 4887 .
- Raslan , K. R. 1999 . “ Numerical methods for partial differential equations ” . Cairo : Al-Azhar University . Ph.D. Thesis
- Abdulloev , Kh. O. , Bogalubsky , I. L. and Makhankov , V. G. 1976 . One more example of inelastic solution interaction . Physics Letters , 56A : 427 – 428 .
- Elibeck , J. C. and McGuire , G. R. 1977 . Numerical study of the RLW equation. II: Interaction of solitary waves . Journal of Computational Physics , 23 : 63 – 73 .
- Gardner , L. R.T. and Gardner , G. A. 1990 . Solitary waves of RLW equation . Journal of Computational Physics , 91 : 441 – 459 .
- Jain , P. C. , Shankar , R. and Singh , T. V. 1993 . Numerical solutions of RLW equation . Communications on Numerical Methods in Engineering , 9 : 587 – 594 .
- Gardner , L. R.T. , Gardner , G. A. and Dogan , A. 1996 . A least-squares FE scheme for the RLW equation . Communications on Numerical Methods in Engineering , 12 : 795 – 804 .
- Saki , S. I. 2001 . Solitary waves of the splitted RLW equation . Computational Physics Communications , 138 : 80 – 91 .
- Whitham , G. B. 1974 . Linear and Nonlinear Waves , New York : John Wiley .
- Rizun , V. I. and Engel’brekht , Iu. K. 1976 . Application of the Burgers’ equation with a variable coefficient to study of nonplanar wave transients . PMM Journal of Applied Mathematics , 39 : 524
- Fried , J. J. and Combarnous , M. A. 1971 . Dispersion in porous media . Advances in Hydroscience , 7 : 169
- Fletcher , C. J. 1983 . A Comparison of finite element and finite difference solutions of one- and two-dimensional Burgers’ equations . Journal of Computational Physics , 51 : 159
- Ten Thije Boonkkamp , J. H.M. and Verwer , J. G. 1987 . On the odd–even hopscotch for the numerical integration of time dependent partial differential equation . Applied Numerical Mathematics , 3 : 183
- Arminjon , P. and Beauchamp , C. 1979 . Numerical solution of Burgers’ equations in two space dimensions . Computer Methods in Applied Mechanics and Engineering , 19 ( 3 ) : 351
- Jain , P. C. and Raja , M. 1979 . Splitting-up technique for Burgers’ equations . Indian Journal of Pure and Applied Mathematics , 10 : 1545
- Jain , P. C. and Lohar , B. L. 1979 . Cubic spline technique for coupled nonlinear parabolic equations . Computation and Mathematics with Applications , 5 : 179
- El-Zoheiry , H. and El-Naggar , B. B. Numerical study of the two dimensional Burgers’ equations using the cubic spline approximations . Proceedings of the 2nd International Conference on Engineering, Mathematics and Physics, Cairo University , Vol. 3 , pp. 363
- El-Naggar , B. B. 1997 . SADI spline alternating direction implicit method for solving the coupled Burgers’ equations . Alexandria Engineering Journal , 36 : 19
- Radwan , S. F. 1999 . On the fourth-order accurate compact ADI scheme for solving the unsteady nonlinear coupled Burgers’ equations . Journal of Nonlinear Mathematical Physics , 6 : 13 – 34 .