References
- N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337–404, 1950. http://dx.doi.org/10.1090/S0002-9947-1950-0051437-7.
- R. Chen and Z. Wu. Solving partial differential equation by using multiquadric quasi-interpolation. Appl. Math. Comput., 6:1502–1510, 2007. http://dx.doi.org/10.1016/j.amc.2006.07.160.
- M. Cui and Y. Lin. Nonlinear Numerical Analysis in Reproducing Kernel Space. Nova Science Pub. Inc., 2009.
- L. Debnath and P. Mikusiński. Hilbert Spaces with Applications. Elsevier Academic Press, USA, 2005.
- M. Dehghan and A. Taleei. A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrödinger equations. Comput. Phys. Comm., 182:2519–2529, 2011. http://dx.doi.org/10.1016/j.cpc.2011.07.009.
- F. Geng and X.M. Li. A new method for Riccati differential equations based on reproducing kernel and quasilinearization methods. Abstr. Appl. Anal., 2012. http://dx.doi.org/10.1155/2012/603748. Article ID 603748
- S. Islam, H. Sirajul and U. Marjan. A meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations. Eng. Anal. Boundary Elem., 33:399–409, 2009. http://dx.doi.org/10.1016/j.enganabound.2008.06.005.
- D. Kaya. An explicit solution of coupled viscous Burgers’ equation by the decomposition method. IJMMS, 11:675–680, 2001.
- A.H. Khater, R.S. Temsah and M.S. Hassan. A Chebyshev spectral collocation method for solving Burgers’-type equations. J. Comput. Appl. Math., 222:333–350, 2008. http://dx.doi.org/10.1016/j.cam.2007.11.007.
- R.C. Mittal and G. Arora. Numerical solution of the coupled viscous Burgers’ equation. Commun. Nonlinear Sci. Numer. Simul., 15:1304–1313, 2011. http://dx.doi.org/10.1016/j.cnsns.2010.06.028.
- M. Mohammadi and R. Mokhtari. Solving the generalized regularized long wave equation on the basis of a reproducing kernel space. J. Comput. Appl. Math., 235:4003–4014, 2011. http://dx.doi.org/10.1016/j.cam.2011.02.012.
- M. Mohammadi and R. Mokhtari. A new algorithm for solving one-dimensional Schrödinger equations in the reproducing kernel space. IJS&T-Transaction A., 37:546–523, 2013.
- R. Mokhtari and M. Mohammadi. New exact solutions to a class of coupled nonlinearPDEs. Int. J. Nonlinear Sci. Numer. Simul., 10:779–796, 2009. http://dx.doi.org/10.1515/IJNSNS.2009.10.6.779
- R. Mokhtari and M. Mohammadi. Numerical solution of GRLW equation using Sinc-collocation method. Comput. Phys. Comm., 181:1266–1274, 2010. http://dx.doi.org/10.1016/j.cpc.2010.03.015.
- R. Mokhtari and M. Mohseni. A meshless method for solving mKdV equation. Comput. Phys. Comm., 183:1259–1268, 2012. http://dx.doi.org/10.1016/j.cpc.2012.02.006.
- R. Mokhtari, F. Toutian Isfahani and M. Mohammadi. Solving a class of nonlinear differential-difference equations in the reproducing kernel space. Abstr. Appl. Anal., 2012. Article ID 514103
- J. Nee and J. Duan. Limit set of trajectories of the coupled viscous Burgers’ equations. Appl. Math. Lett., 11:57–61, 1998. http://dx.doi.org/10.1016/S0893-9659(97)00133-X.
- A. Rashid and A. Ismail. A Fourier pseudospectral method for solving coupled viscous Burgers’ equations. Comput. Methods Appl. Math., 9:412–420, 2009.
- A. Soliman. The modified extended tanh-function method for solving Burgers’ type equations. Phys. A, 361:394–404, 2006. http://dx.doi.org/10.1016/j.physa.2005.07.008.
- S.M. Wong, Y.C. Hon and M.A. Golberg. Compactly supported radial basis functions for shallow water equations. Appl. Math. Comput., 127:70–101, 2002. http://dx.doi.org/10.1016/S0096-3003(01)00006-6.
- L. Yingzhen and Z. Yongfang. Solving nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space. Numer. Algorithms, 52:173–186, 2009. http://dx.doi.org/10.1007/s11075-009-9263-6.