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Study of Stability Analysis for a Class of Fourth Order Boundary Value Problems
Department of Mathematics, Chaitanya Degree College (Autonomous), Warangal, India
Department of Mathematics, Kakatiya Institute of Technology & Science, Warangal, India
- 1 Department of Mathematics, Chaitanya Degree College (Autonomous), Warangal, India
- 2 Department of Mathematics, Kakatiya Institute of Technology & Science, Warangal, India
Applied Mathematics·Volume 05 (2014)·Pages 1887–1893·Published 7 July 2014·DOI10.4236/am.2014.513182
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Abstract
Fourth order differential equations are considered to develop the class of methods for the numerical solution of boundary value problems. In this paper, we have discussed the regions of absolute stability of fourth order boundary value problems. Methods proposed and derived in this paper are applied to solve a fourth-order boundary value problem. Numerical results are given to illustrate the efficiency of our methods and compared with exact solution.
KeywordsNumerical DifferentiationInitial Value ProblemBoundary Value ProblemAbsolute StabilityMultistep Methods
- Bala Rama Krishna, C., Rama Chandra Rao, P.S., Vishwa Prasad Rao, S. and Nageswara Rao, B. (2013) Finite Difference Methods for the Solution of a Class of Singular Perturbation Problems. International Journal of Mathematical Sciences and Engineering Applications, 7, 411-421
- Eskandari, Z. and Dahaghin, M.S. (2012) A Special Linear Multi Step Method for Special Second Order Differenial Equations. International Journal of Pure and Applied Mathematics, 78, 1-8.
- Gear, C.W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall, Upper Saddle River.
- Gragg, W.B. and Statter, H.J. (1964) Generalized Multistep Predictor-Corrector Methods. Journal of the ACM, 11, 188-209. http://dx.doi.org/10.1145/321217.321223
- Henrici, P. (1962) Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York.
- Jain, M.K. (1984) Numerical Solution of Differential Equations. Wiley Eastern Ltd., New Delhi.
- Kalyani, P. and Rama Chandra Rao, P.S. (2013) Solution of Boundary Value Problems by Approaching Spline Techniques. International Journal of Engineering Mathematics, 2013, Article ID: 482050.
- Kalyani, P. and Rama Chandra Rao, P.S. (2013) A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions. Applied Mathematics, 2013, 583-588.
- Rama Chandra Rao, P.S. (2006) Special Multistep Methods Based on Numerical Differentiation for Solving the Initial Value Problem. Applied Mathematics and Computation, 181, 500-510. http://dx.doi.org/10.1016/j.amc.2005.12.063