Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 302936, 6 pages.
A New Numerical Algorithm for Two-Point Boundary Value Problems
Lihua Guo, Boying Wu, and Dazhi Zhang
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Abstract
We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.
Article information
Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 302936, 6 pages.
Dates
First available in Project Euclid: 6 October 2014
Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606418
Digital Object Identifier
doi:10.1155/2014/302936
Mathematical Reviews number (MathSciNet)
MR3230515
Zentralblatt MATH identifier
07022119
Citation
Guo, Lihua; Wu, Boying; Zhang, Dazhi. A New Numerical Algorithm for Two-Point Boundary Value Problems. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 302936, 6 pages. doi:10.1155/2014/302936. https://projecteuclid.org/euclid.aaa/1412606418
References
- T. Aziz and M. Kumar, “A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 136, no. 1-2, pp. 337–342, 2001.Mathematical Reviews (MathSciNet): MR1855902
Digital Object Identifier: doi:10.1016/S0377-0427(00)00624-5 - M. Kumar and T. Aziz, “A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems,” International Journal of Computer Mathematics, vol. 81, no. 12, pp. 1507–1512, 2004.Mathematical Reviews (MathSciNet): MR2169100
Zentralblatt MATH: l1063.65068
Digital Object Identifier: doi:10.1080/00207160412331284097 - M. Kumar, “A second order spline finite difference method for singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 142, no. 2-3, pp. 283–290, 2003.Mathematical Reviews (MathSciNet): MR1979435
Zentralblatt MATH: l1034.65061
Digital Object Identifier: doi:10.1016/S0096-3003(02)00302-8 - M. Kumar, “Higher order method for singular boundary-value problems by using spline function,” Applied Mathematics and Computation, vol. 192, no. 1, pp. 175–179, 2007.Mathematical Reviews (MathSciNet): MR2385581
Digital Object Identifier: doi:10.1016/j.amc.2007.02.156 - J. Rashidinia, Z. Mahmoodi, and M. Ghasemi, “Parametric spline method for a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 58–63, 2007.Mathematical Reviews (MathSciNet): MR2327093
Zentralblatt MATH: l1114.65341
Digital Object Identifier: doi:10.1016/j.amc.2006.09.084 - H. Yao and Y. Lin, “Solving singular boundary-value problems of higher even-order,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 703–713, 2009.Mathematical Reviews (MathSciNet): MR2478873
Zentralblatt MATH: l1181.65108
Digital Object Identifier: doi:10.1016/j.cam.2008.02.010 - Y. Lin, J. Niu, and M. Cui, “A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7362–7368, 2012.Mathematical Reviews (MathSciNet): MR2892704
Digital Object Identifier: doi:10.1016/j.amc.2011.11.009 - J. Niu, Y. Z. Lin, and C. P. Zhang, “Approximate solution of nonlinear multi-point boundary value problem on the half-line,” Mathematical Modelling and Analysis, vol. 17, no. 2, pp. 190–202, 2012.Mathematical Reviews (MathSciNet): MR2904363
Digital Object Identifier: doi:10.3846/13926292.2012.660889 - C. Song, J. Li, and R. Gao, “Nonexistence of global solutions to the initial boundary value problem for the singularly perturbed sixth-order boussinesq -type equation,” Journal of Applied Mathematics, vol. 2014, Article ID 928148, 7 pages, 2014.Mathematical Reviews (MathSciNet): MR3216140
- B. Orel and A. Perne, “Chebyshev-fourier spectral methods for nonperiodic boundary value problems,” Journal of Applied Mathematics, vol. 2014, Article ID 572694, 10 pages, 2014.Mathematical Reviews (MathSciNet): MR3219423
Zentralblatt MATH: 1304.49046
Digital Object Identifier: doi:10.1155/2014/572694 - N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950.Mathematical Reviews (MathSciNet): MR0051437
Zentralblatt MATH: l0037.20701
Digital Object Identifier: doi:10.1090/S0002-9947-1950-0051437-7 - M. G. Cui and Y. Z. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel, Nova Science, New York, NY, USA, 2009.
- R. K. Pandy and Singh. A. K., “On the convergence of second-order finite difference method for weakly regular singular boundary value problems,” International Journal of Computer Mathematics, vol. 85, no. 12, pp. 1807–1814, 2008.
- A. E. Ebaid, “Exact solutions for a class of nonlinear singular two-point boundary value problems: the decomposition method,” Zeitschrift fur Naturforschung A: Journal of Physical Sciences, vol. 65, no. 3, pp. 145–150, 2010.
- A. Ebaid, “A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 1914–1924, 2011.Mathematical Reviews (MathSciNet): MR2763114
Zentralblatt MATH: l1209.65077
Digital Object Identifier: doi:10.1016/j.cam.2010.09.007 - S. M. El-Sayed, “Integral methods for computing solutions of a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 130, no. 2-3, pp. 235–241, 2002. \endinputMathematical Reviews (MathSciNet): MR1912209
Digital Object Identifier: doi:10.1016/S0096-3003(01)00091-1
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