**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33011

##### An Efficient Method for Solving Multipoint Equation Boundary Value Problems

**Authors:**
Ampon Dhamacharoen,
Kanittha Chompuvised

**Abstract:**

**Keywords:**
Boundary value problem; Multipoint equation
boundary value problems,
Shooting Method,
Newton-Broyden
method.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334449

**References:**

[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. Dul├ícska, 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.