Radial basis functions method for numerical solution of the modified equal width equation

The numerical solution of the modified equal width equation is investigated by using meshless method based on collocation with the well-known radial basis functions. Single solitary wave motion, two solitary waves interaction and three solitary waves interaction are studied. Results of the meshless methods with different radial basis functions are presented.

[1]  Benny Y. C. Hon,et al.  An efficient numerical scheme for Burgers' equation , 1998, Appl. Math. Comput..

[2]  I. Dag,et al.  Numerical solutions of KdV equation using radial basis functions , 2008 .

[3]  Alaattin Esen,et al.  A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines , 2006, Int. J. Comput. Math..

[4]  S. Zaki.  Solitary wave interactions for the modified equal width equation , 2000 .

[5]  S. Kutluay,et al.  Solitary wave solutions of the modified equal width wave equation , 2008 .

[6]  Jichun Li,et al.  Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling , 2003 .

[7]  Bülent Saka,et al.  Algorithms for numerical solution of the modified equal width wave equation using collocation method , 2007, Math. Comput. Model..

[8]  Carsten Franke,et al.  Solving partial differential equations by collocation using radial basis functions , 1998, Appl. Math. Comput..

[9]  A. Wazwaz.  THE TANH AND THE SINE–COSINE METHODS FOR A RELIABLE TREATMENT OF THE MODIFIED EQUAL WIDTH EQUATION AND ITS VARIANTS , 2006 .

[10]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[11]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[12]  Y. C. Hon,et al.  Numerical comparisons of two meshless methods using radial basis functions , 2002 .

[13]  David J. Evans,et al.  Solitary waves for the generalized equal width (GEW) equation , 2005, Int. J. Comput. Math..

[14]  Junfeng Lu,et al.  He’s variational iteration method for the modified equal width equation , 2009 .

[15]  S. G. Rubin,et al.  A cubic spline approximation for problems in fluid mechanics , 1975 .

[16]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[17]  James D. Meiss,et al.  SCATTERING OF REGULARIZED-LONG-WAVE SOLITARY WAVES , 1984 .

[18]  Scott A. Sarra,et al.  Adaptive radial basis function methods for time dependent partial differential equations , 2005 .

[19]  Idris Dag,et al.  Numerical solution of RLW equation using radial basis functions , 2010, Int. J. Comput. Math..

[20]  Alper Korkmaz,et al.  Three different methods for numerical solution of the EW equation , 2008 .