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The use of sinc-collocation method for solving multi-point boundary value problems. (English) Zbl 1244.65114
Summary: Multi-point boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering. In this work, our goal is to obtain numerically the approximate solution of these problems by using the sinc-collocation method. Some properties of the sinc-collocation method required for our subsequent development are given and are utilized to reduce the computation of solution of multi-point boundary value problems to some algebraic equations. It is well known that the sinc procedure converges to the solution at an exponential rate. Numerical examples are included to demonstrate the validity and applicability of the new technique.
65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
[1]Stenger, F.: Numerical methods based on sinc and analytic functions, (1993)
[2]Lund, J.; Bowers, K.: Sinc methods for quadrature and differential equations, (1992) · Zbl 0753.65081
[3]Winter, D. F.; Bowers, K.; Lund, J.: Wind-driven currents in a sea with a variable eddy viscosity calculated via a sinc – Galerkin technique, Int J numer methods fluids 33, 1041-1073 (2000) · Zbl 0984.76066 · doi:10.1002/1097-0363(20000815)33:7<1041::AID-FLD42>3.0.CO;2-P
[4]Bialecki, B.: Sinc-collocation methods for two-point boundary value problems, IMA J numer anal 11, 357-375 (1991) · Zbl 0735.65052 · doi:10.1093/imanum/11.3.357
[5]Parand, K.; Pirkhedri, A.: Sinc-collocation method for solving astrophysics equations, New astron 15, 533-537 (2010)
[6]Parand, K.; Dehghan, M.; Pirkhedri, A.: Sinc-collocation method for solving the Blasius equation, Phys lett A 373, 4060-4065 (2009)
[7]Parand, K.; Delafkar, Z.; Pakniat, N.; Pirkhedri, A.; Haji, M. Kazemnasab: Collocation method using sinc and rational Legendre functions for solving Volterra’s population model, Commun nonlinear sci numer simulat 16, 1811-1819 (2011) · Zbl 1221.65186 · doi:10.1016/j.cnsns.2010.08.018
[8]Saadatmandi, A.; Razzaghi, M.; Dehghan, M.: Sinc-collocation methods for the solution of hallen’s integral equation, J electromagan waves appl 19, No. 2, 245-256 (2005)
[9]Saadatmandi, A.; Razzaghi, M.: The numerical solution of third-order boundary value problems using sinc-collocation method, Commun numer meth eng 23, 681-689 (2007) · Zbl 1121.65088 · doi:10.1002/cnm.918
[10]Dehghan, M.; Saadatmandi, A.: The numerical solution of a nonlinear system of second-order boundary value problems using the sinc-collocation method, Math comput model 46, 1434-1441 (2007) · Zbl 1133.65050 · doi:10.1016/j.mcm.2007.02.002
[11]El-Gamel, M.; Behiry, S. H.; Hashish, H.: Numerical method for the solution of special nonlinear fourth – order boundary value problems, Appl math comput 145, 717-734 (2003) · Zbl 1033.65065 · doi:10.1016/S0096-3003(03)00269-8
[12]Alain, P. N. Dinh; Quan, P. H.; Trong, D. D.: Sinc approximation of the heat distribution on the boundary of a two-dimensional finite slab, Nonlinear anal: real world appl 9, 1103-1111 (2008) · Zbl 1146.35376 · doi:10.1016/j.nonrwa.2007.02.009
[13]Abdella, K.; Yu, X.; Kucuk, I.: Application of the sinc method to a dynamic elasto-plastic problem, J comput appl math 223, 626-645 (2009) · Zbl 1153.74051 · doi:10.1016/j.cam.2008.02.003
[14]Lund, J.; Vogel, C. R.: A fully-Galerkin method for the numerical solution of an inverse problem in a parabolic partial differential equation, Inverse probl 6, 205-217 (1990) · Zbl 0709.65104 · doi:10.1088/0266-5611/6/2/005
[15]Shidfar, A.; Zolfaghari, R.; Damirchi, J.: Application of sinc-collocation method for solving an inverse problem, J comput appl math 223, 545-554 (2009) · Zbl 1180.65118 · doi:10.1016/j.cam.2009.08.003
[16]Rashidinia, J.; Zarebnia, M.: The numerical solution of integro-differential equation, Appl math comput 188, 1124-1130 (2007) · Zbl 1118.65131 · doi:10.1016/j.amc.2006.10.063
[17]Mohsen, A.; El – Gamel, M.: On the numerical solution of linear and nonlinear Volterra integral and integro-differential equations, Appl math comput 217, 3330-3337 (2010) · Zbl 1204.65158 · doi:10.1016/j.amc.2010.08.065
[18]El – Gamel, M.; Zayed, A.: Sinc – Galerkin method for solving nonlinear boundary-value problems, Comput math appl 48, 1285-1298 (2004) · Zbl 1072.65111 · doi:10.1016/j.camwa.2004.10.021
[19]Revelli, R.; Ridolfi, L.: Sinc collocation-interpolation method for the simulation of nonlinear waves, Comput math appl 46, 1443-1453 (2003) · Zbl 1049.65107 · doi:10.1016/S0898-1221(03)90232-X
[20]Mohsen, A.; El – Gamel, M.: A sinc-collocation method for the linear Fredholm integro-differential equations, Z angew mat phys 58, 380-390 (2007) · Zbl 1116.65131 · doi:10.1007/s00033-006-5124-5
[21]Mohsen, A.; El – Gamel, M.: On the Galerkin and collocation methods for two-point boundary value problems using sinc bases, Comput math appl 56, 930-941 (2008) · Zbl 1155.65365 · doi:10.1016/j.camwa.2008.01.023
[22]Muhammad, M.; Nurmuhammad, A.; Mori, M.; Sugihara, M.: Numerical solution of integral equations by means of the sinc-collocation method based on the double exponential transformation, J comput appl math 177, 269-286 (2005) · Zbl 1072.65168 · doi:10.1016/j.cam.2004.09.019
[23]Sababheh, M. S.; Al-Khaled, A. M. N.: Some convergence results on sinc interpolation, J inequal pure appl math 4, 32-48 (2003) · Zbl 1069.41005
[24]Hajji MA. Multi-point special boundary-value problems and applications to fluid flow through porous media, In: Proceedings of the International Multi-Conference of Engineers and Computer Scientists 2009, vol II, Hong Kong.
[25]Il’in, V. A.; Moiseev, E. I.: Nonlocal boundary value problem of the first kind for a Sturm – Liouville operator in its differential and finite difference aspects, Differ equ 23, No. 7, 803-810 (1987) · Zbl 0668.34025
[26]Il’in, V. A.; Moiseev, E. I.: Nonlocal boundary value problem of the second kind for a Sturm – Liouville operator, Differ equ 23, No. 8, 979-987 (1987) · Zbl 0668.34024
[27]Gupta, C. P.: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, J math anal appl 168, 540-551 (1992) · Zbl 0763.34009 · doi:10.1016/0022-247X(92)90179-H
[28]Ma, R.: A survey on nonlocal boundary value problems, Appl math E-notes 7, 257-279 (2007) · Zbl 1163.34300 · doi:emis:journals/AMEN/2007/2007.htm
[29]Moshinsky, M.: Sobre los problems de condiciones a la frontiera en una dimension de carac-teristicas discontinuas, Bol soc mat mexicana 7, 1-25 (1950)
[30]Timoshenko, S.: Theory of elastic stability, (1961)
[31]Geng, F.; Cui, M.: Multi-point boundary value problem for optimal Bridge design, Int J comput math 87, 1051-1056 (2010) · Zbl 1192.65109 · doi:10.1080/00207160903023573
[32]Bai, C.; Fang, J.: Existence of multiple positive solutions for nonlinear m-point boundary value problems, J math anal appl 281, 76-85 (2003) · Zbl 1030.34026 · doi:10.1016/S0022-247X(02)00453-5
[33]Lentini, M.; Pereyra, V.: A variable order finite difference method for nonlinear multi-point boundary value problems, Math comput 28, 981-1003 (1974) · Zbl 0308.65054 · doi:10.2307/2005360
[34]Dehghan, M.: Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices, Math comput simulat 71, 16-30 (2006) · Zbl 1089.65085 · doi:10.1016/j.matcom.2005.10.001
[35]Zou, Y.; Hu, Q.; Zhang, R.: On numerical studies of multi-point boundary value problems and its fold bifurcation, Appl math comput 185, 527-537 (2007) · Zbl 1112.65069 · doi:10.1016/j.amc.2006.07.064
[36]Tatari, M.; Dehghan, M.: The use of the Adomian decomposition method for solving multi-point boundary value problems, Phys scripta 73, 672-676 (2006)
[37]Dehghan M, Shakeri F. A semi-numerical technique for solving the multi-point boundary value problems and engineering applications. Int J Numer Methods Heat Fluid Flow, in press
[38]Ali, J.; Islam, S.; Zaman, G.: The solution of multi-point boundary value problems by the optimal homotopy asymptotic method, Comput math appl 59, 2000-2006 (2010) · Zbl 1189.65154 · doi:10.1016/j.camwa.2009.12.002
[39]Tatari M, Dehghan M, An efficient method for solving multi-point boundary value problems and applications in physics, J Vibr Contr, in press, lt;doi: 10.1177/1077546311408467gt;
[40]Haque, M.; Baluch, M. H.; Mohsen, M. F. N.: Solution of multiple point, nonlinear boundary value problems by method of weighted residuals, Int J comput math 19, 69-84 (1986) · Zbl 0653.65059 · doi:10.1080/00207168608803505