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Reproducing kernel functions for difference equations
1. | Siirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, Turkey |
2. | Fırat University, Science Faculty, Department of Mathematics, 23119 Elazıǧ, Turkey, Turkey |
References:
[1] |
S. Abbasbandy, B. Azarnavid and M. S. Alhuthali, A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, J. Comput. Appl. Math., 279 (2015), 293-305.
doi: 10.1016/j.cam.2014.11.014. |
[2] |
M. Adivar, H. C. Koyuncuoǧlu and Y. N. Raffoul, Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay, J. Difference Equ. Appl., 19 (2013), 1927-1939.
doi: 10.1080/10236198.2013.791688. |
[3] |
R. P. Agarwal, Difference Equations and Inequalities, $2^{nd}$ edition, Monographs and Textbooks in Pure and Applied Mathematics, 228, Marcel Dekker Inc., New York, 2000. |
[4] |
A. Akgül, A new method for approximate solutions of fractional order boundary value problems, Neural Parallel Sci. Comput., 22 (2014), 223-237. |
[5] |
A. Akgül, M. Inc, E. Karatas and D. Baleanu, Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique, Adv. Difference Equ., 2015 (2015), 12pp.
doi: 10.1186/s13662-015-0558-8. |
[6] |
S. S. Cheng and W. T. Patula, An existence theorem for a nonlinear difference equation, Nonlinear Anal., 20 (1993), 193-203.
doi: 10.1016/0362-546X(93)90157-N. |
[7] |
M. Cui and Z. X. Deng, On the best operator of interpolation in $W_2^1$, Math. Numer. Sinica, 8 (1986), 209-216. |
[8] |
M. Cui and H. Du, Representation of exact solution for the nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 182 (2006), 1795-1802.
doi: 10.1016/j.amc.2006.06.016. |
[9] |
M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science Publishers Inc., New York, 2009. |
[10] |
S. N. Elaydi, An Introduction to Difference Equations, Second edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999.
doi: 10.1007/978-1-4757-3110-1. |
[11] |
R. A. C. Ferreira and D. F. M. Torres, Fractional h-difference equations arising from the calculus of variations, Appl. Anal. Discrete Math., 5 (2011), 110-121.
doi: 10.2298/AADM110131002F. |
[12] |
F. Z. Geng, A numerical algorithm for nonlinear multi-point boundary value problems, J. Comput. Appl. Math., 236 (2012), 1789-1794.
doi: 10.1016/j.cam.2011.10.010. |
[13] |
F. Geng, A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems, Appl. Math. Comput., 213 (2009), 163-169.
doi: 10.1016/j.amc.2009.02.053. |
[14] |
F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327 (2007), 1167-1181.
doi: 10.1016/j.jmaa.2006.05.011. |
[15] |
F. Geng and M. Cui, New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions, J. Math. Anal. Appl., 233 (2009), 165-172.
doi: 10.1016/j.cam.2009.07.007. |
[16] |
P. Hartman and A. Wintner, On linear difference equations of second order, Amer. J. Math., 72 (1950), 124-128.
doi: 10.2307/2372138. |
[17] |
M. Inc and A. Akgül, Approximate solutions for MHD squeezing fluid flow by a novel method, Bound. Value Probl., 2014 (2014), 17pp.
doi: 10.1186/1687-2770-2014-18. |
[18] |
M. Inc, A. Akgül and A. Kilicman, Numerical solutions of the secondorder one-dimensional telegraph equation based on reproducing kernel Hilbert space method, Abstr. Appl. Anal., (2013), Art. ID 768963, 13pp. |
[19] |
S. Javadi, E. Babolian and E. Moradi, New implementation of reproducing kernel Hilbert space method for solving a class of functional integral equations, Commun. Numer. Anal., (2014), Art. ID 00205, 7pp. |
[20] |
W. G. Kelley and A. C. Peterson, Difference Equations. An Introduction with Applications, Second edition, Harcourt/Academic Press, San Diego, CA, 2001. |
[21] |
R. Ketabchi, R. Mokhtari and E. Babolian, Some error estimates for solving Volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math., 273 (2015), 245-250.
doi: 10.1016/j.cam.2014.06.016. |
[22] |
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 (2011), 4003-4014.
doi: 10.1016/j.cam.2011.02.012. |
[23] |
M. N. Phong, A note on a system of two nonlinear difference equations, Electron. J. Math. Anal. Appl., 3 (2015), 170-179. |
[24] |
J. Popenda and E. Schmeidel, Some properties of solutions of difference equations, Fasc. Math., 13 (1981), 89-98. |
[25] |
R. Salehi and M. Dehghan, A generalized moving least square reproducing kernel method, J. Comput. Appl. Math., 249 (2013), 120-132.
doi: 10.1016/j.cam.2013.02.005. |
[26] |
K. Seddighi, Reproducing kernel Hilbert spaces, Iranian J. Sci. Tech., 17 (1993), 171-177. |
[27] |
S. S. Shishvan, A. Noorzad and A. Ansari, A time integration algorithm for linear transient analysis based on the reproducing kernel method, Comput. Methods Appl. Mech. Engrg., 198 (2009), 3361-3377.
doi: 10.1016/j.cma.2009.06.011. |
[28] |
Q. Zhang and W. Zhang, On a system of two high-order nonlinear difference equations, Adv. Math. Phys., (2014), Art. ID 729273, 8pp.
doi: 10.1155/2014/729273. |
show all references
References:
[1] |
S. Abbasbandy, B. Azarnavid and M. S. Alhuthali, A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, J. Comput. Appl. Math., 279 (2015), 293-305.
doi: 10.1016/j.cam.2014.11.014. |
[2] |
M. Adivar, H. C. Koyuncuoǧlu and Y. N. Raffoul, Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay, J. Difference Equ. Appl., 19 (2013), 1927-1939.
doi: 10.1080/10236198.2013.791688. |
[3] |
R. P. Agarwal, Difference Equations and Inequalities, $2^{nd}$ edition, Monographs and Textbooks in Pure and Applied Mathematics, 228, Marcel Dekker Inc., New York, 2000. |
[4] |
A. Akgül, A new method for approximate solutions of fractional order boundary value problems, Neural Parallel Sci. Comput., 22 (2014), 223-237. |
[5] |
A. Akgül, M. Inc, E. Karatas and D. Baleanu, Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique, Adv. Difference Equ., 2015 (2015), 12pp.
doi: 10.1186/s13662-015-0558-8. |
[6] |
S. S. Cheng and W. T. Patula, An existence theorem for a nonlinear difference equation, Nonlinear Anal., 20 (1993), 193-203.
doi: 10.1016/0362-546X(93)90157-N. |
[7] |
M. Cui and Z. X. Deng, On the best operator of interpolation in $W_2^1$, Math. Numer. Sinica, 8 (1986), 209-216. |
[8] |
M. Cui and H. Du, Representation of exact solution for the nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 182 (2006), 1795-1802.
doi: 10.1016/j.amc.2006.06.016. |
[9] |
M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science Publishers Inc., New York, 2009. |
[10] |
S. N. Elaydi, An Introduction to Difference Equations, Second edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999.
doi: 10.1007/978-1-4757-3110-1. |
[11] |
R. A. C. Ferreira and D. F. M. Torres, Fractional h-difference equations arising from the calculus of variations, Appl. Anal. Discrete Math., 5 (2011), 110-121.
doi: 10.2298/AADM110131002F. |
[12] |
F. Z. Geng, A numerical algorithm for nonlinear multi-point boundary value problems, J. Comput. Appl. Math., 236 (2012), 1789-1794.
doi: 10.1016/j.cam.2011.10.010. |
[13] |
F. Geng, A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems, Appl. Math. Comput., 213 (2009), 163-169.
doi: 10.1016/j.amc.2009.02.053. |
[14] |
F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327 (2007), 1167-1181.
doi: 10.1016/j.jmaa.2006.05.011. |
[15] |
F. Geng and M. Cui, New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions, J. Math. Anal. Appl., 233 (2009), 165-172.
doi: 10.1016/j.cam.2009.07.007. |
[16] |
P. Hartman and A. Wintner, On linear difference equations of second order, Amer. J. Math., 72 (1950), 124-128.
doi: 10.2307/2372138. |
[17] |
M. Inc and A. Akgül, Approximate solutions for MHD squeezing fluid flow by a novel method, Bound. Value Probl., 2014 (2014), 17pp.
doi: 10.1186/1687-2770-2014-18. |
[18] |
M. Inc, A. Akgül and A. Kilicman, Numerical solutions of the secondorder one-dimensional telegraph equation based on reproducing kernel Hilbert space method, Abstr. Appl. Anal., (2013), Art. ID 768963, 13pp. |
[19] |
S. Javadi, E. Babolian and E. Moradi, New implementation of reproducing kernel Hilbert space method for solving a class of functional integral equations, Commun. Numer. Anal., (2014), Art. ID 00205, 7pp. |
[20] |
W. G. Kelley and A. C. Peterson, Difference Equations. An Introduction with Applications, Second edition, Harcourt/Academic Press, San Diego, CA, 2001. |
[21] |
R. Ketabchi, R. Mokhtari and E. Babolian, Some error estimates for solving Volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math., 273 (2015), 245-250.
doi: 10.1016/j.cam.2014.06.016. |
[22] |
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 (2011), 4003-4014.
doi: 10.1016/j.cam.2011.02.012. |
[23] |
M. N. Phong, A note on a system of two nonlinear difference equations, Electron. J. Math. Anal. Appl., 3 (2015), 170-179. |
[24] |
J. Popenda and E. Schmeidel, Some properties of solutions of difference equations, Fasc. Math., 13 (1981), 89-98. |
[25] |
R. Salehi and M. Dehghan, A generalized moving least square reproducing kernel method, J. Comput. Appl. Math., 249 (2013), 120-132.
doi: 10.1016/j.cam.2013.02.005. |
[26] |
K. Seddighi, Reproducing kernel Hilbert spaces, Iranian J. Sci. Tech., 17 (1993), 171-177. |
[27] |
S. S. Shishvan, A. Noorzad and A. Ansari, A time integration algorithm for linear transient analysis based on the reproducing kernel method, Comput. Methods Appl. Mech. Engrg., 198 (2009), 3361-3377.
doi: 10.1016/j.cma.2009.06.011. |
[28] |
Q. Zhang and W. Zhang, On a system of two high-order nonlinear difference equations, Adv. Math. Phys., (2014), Art. ID 729273, 8pp.
doi: 10.1155/2014/729273. |
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