Reproducing kernel functions for difference equations

In this work, some new reproducing kernel functions for difference equations are found. Reproducing kernel functions have not been obtained for difference equations until now. We need these functions to solve difference equations with the reproducing kernel method. Therefore, these functions are very considerable functions.

[1]  Esmail Babolian,et al.  Some error estimates for solving Volterra integral equations by using the reproducing kernel method , 2015, J. Comput. Appl. Math..

[2]  Hong Du,et al.  Representation of exact solution for the nonlinear Volterra-Fredholm integral equations , 2006, Appl. Math. Comput..

[3]  P. Hartman,et al.  Errata: On Linear Difference Equations of Second Order , 1950 .

[4]  F. Z. Geng A numerical algorithm for nonlinear multi-point boundary value problems , 2012, J. Comput. Appl. Math..

[5]  Y. Raffoul,et al.  Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay , 2013, 1303.6827.

[6]  Fazhan Geng,et al.  Solving a nonlinear system of second order boundary value problems , 2007 .

[7]  Minggen Cui,et al.  Nonlinear Numerical Analysis in Reproducing Kernel Space , 2009 .

[8]  Maryam Mohammadi,et al.  Solving the generalized regularized long wave equation on the basis of a reproducing kernel space , 2011, J. Comput. Appl. Math..

[9]  Delfim F. M. Torres,et al.  FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS , 2011, 1101.5904.

[10]  Qianhong Zhang,et al.  On a System of Two High-Order Nonlinear Difference Equations , 2014 .

[11]  Fazhan Geng,et al.  New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions , 2009, J. Comput. Appl. Math..

[12]  S. S. Shishvan,et al.  A time integration algorithm for linear transient analysis based on the reproducing kernel method , 2009 .

[13]  Baver Okutmustur Reproducing kernel Hilbert spaces , 2005 .

[14]  Sui Sun Cheng,et al.  An existence theorem for a nonlinear difference equation , 1993 .

[15]  Saeid Abbasbandy,et al.  A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems , 2015, J. Comput. Appl. Math..

[17]  Ravi P. Agarwal,et al.  Difference equations and inequalities , 1992 .

[18]  S. Elaydi An introduction to difference equations , 1995 .

[19]  Mehdi Dehghan,et al.  A generalized moving least square reproducing kernel method , 2013, J. Comput. Appl. Math..

[20]  Fazhan Geng,et al.  A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems , 2009, Appl. Math. Comput..

[21]  E. Babolian,et al.  New implementation of reproducing kernel Hilbert space method for solving a class of functional integral equations , 2014 .

[22]  D. Baleanu,et al.  Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique , 2015, Advances in Difference Equations.