- 期刊
FINITE DIFFERENCE METHODS FOR COMPUTING EIGENVALUES OF FOURTH ORDER BOUNDARY VALUE PROBLEMS
摘要
This brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y^(4) (p(x)- λq(x))y =0. These methods are derived from the formula h^4y_1^(4) (δ^4 -1/6 δ^6+7/240 δ^8-….)y_i Numerical results are included to demonstrate practical usefulness of our methods.
延伸閱讀
- Noor, M. A., Said, E. A., & Noor, K. I. (2012). Finite Difference Method for Solving a System of Third-Order Boundary Value Problems. Journal of Applied Mathematics, 2012(), 465-474-234. https://doi.org/10.1155/2012/351764
- USMANI, R. A., & SAKAI, M. (1987). TWO NEW FINITE DIFFERENCE METHODS FOR COMPUTING EIGENVALUES OF A FOURTH ORDER LINEAR BOUNDARY VALUE PROBLEM. International Journal of Mathematics and Mathematical Sciences, 1987(), 525-529. https://doi.org/10.1155/S0161171287000620
- Shi, D. Y., Guan, H. B., & Guan, X. F. (2012). Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality. Journal of Applied Mathematics, 2012(), 689-700-044. https://doi.org/10.1155/2012/156095
- Noor, M. A., & Din, S. T. M. (2007). Variational Iteration Decomposition Method for Solving Eighth-Order Boundary Value Problems. Differential Equations and Nonlinear Mechanics, 2007(), 19-34. https://doi.org/10.1155/2007/19529
- FAYAZOV, K. S., & SCHOCK, E. (2001). BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH OPERATOR COEFFICIENTS. Abstract and Applied Analysis, 2001(), 253-266. https://doi.org/10.1155/S1085337501000628