Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33104
An Efficient Method for Solving Multipoint Equation Boundary Value Problems
Authors: Ampon Dhamacharoen, Kanittha Chompuvised
Abstract:
In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334449
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1786References:
[1] A. Dhamacharoen, "Two-Stage Iteration Methods for Solving Systems of Nonlinear Equations", In The 15th Annual Meeting in Mathematics., Bangkok., Annu. 2010, 6-8.
[2] A. M. Wazwaz, The numerical solution of sixth-order boundary value problems by the modified decomposition method, Appl. Math. Comput. 118 (2001), 311-325.
[3] A. Prachanuruk, Broyden method in solving equations boundary value problems, Master's thesis, Department of Mathematics, Graduate School, Burapha University (2007).
[4] E. Dulácska, Soil Settlement Effects on Buildings,Developments Geotechn. Engrg., vol. 69, Elsevier, Amsterdam,1992.
[5] E. H. Mansfield, The Bending and Stretching of Plates Internat. Ser. Monogr. Aeronautics and Astronautics, vol. 6 Pergamon, New York, 1964.
[6] H. B. Keller, Existence theory for two point boundary value problems, Bull. Amer. Math. Soc., 72 (1966), 728-731.
[7] J. E. Dennis, and R. B. Schnabel, Numerical Methods forUnconstrained Optimization and Nonlinear Equations, SIAM,1966.
[8] J. H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A. 350 (2006), 87-88.
[9] J. H. He, Variational approach to the sixth-order boundaryvalue problems, Appl. Math. Comput. 143 (2-3) (2003), 53-538.
[10] J. Prescott, Applied Elasticity, Dover, New York, 1961.
[11] M. A. Noor, S.T. Mohyud-Din, An efficient algorithm for solving fifthorder boundary value problems, Math. Comput. Model. 45 (7-8) (2007), 954-964.
[12] M. Tatari, M. Dehgan, The use of the Adomian decomposition method for solving multipoint boundary value problems, Phys. Scr. 73 (2006), 672-676.
[13] Q. Yao, Successive iteration and positive solution for nonlinear secondorder three-point boundary value problem, Comput. Math. Appl. 50 (2005), 433-444.
[14] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC, Florida, 2004.
[15] S. N. Ha, A nonlinear shooting method for two-point boundary value problems, Comput. Math. Appl., 42 (10-11) (2001), 1411-1420.
[16] S. P. Timoshenko, Theory of Elastic Stability, McGraw-Hill, New York, 1961.
[17] Siraj-Ul-Islam, I.A. Tirmizi, Fazal-i-Haq, M.A. khan, Non-polynomial splines approach to the solution of sixth-order boundary-value problems, Appl. Math. Comput. 195 (2008), 270-284.
[18] Siraj-Ul-Islam, Sirajul-Haq, Javed Ali, Numerical solution of special 12th-order boundary value problems using differential transform method, Comm. Nonl. Sci. Numeric. Simul. 14 (4) (2009), 1132-1138.
[19] U. M. Ascher, R. M. M. Mattheij, R. D. Russell, Numerical solution of boundary value problems for ordinary differential equations, Englewood Cliffs: Prentice Halll (1988).
[20] W. Jiang, M. Cui, Constructive proof for existence of nonlinear twopoint boundary value problems., Appl. Math. Comput., 215 (5) (2009), 1937-1948.
[21] Y. Tao, G. Gao, Existence, uniqueness and approximation of classical solutions to nonlinear two-point boundary value problems., Nonlinear Anal., 50 (7) (2002), 981-994.
[22] K. Chompuvised, A. Dhamacharoen, Solving boundary value problems of ordinary differential equations with non-separatedboundary conditions, Applied Mathematics and Computation,Volume 217, Issue 24, 15 August 2011, Pages 10355-10360.