A uniformly convergent finite difference method for a singularly perturbed initial value problem

Applied Mathematics and Mechanics (English Edition)

Volumn 20, Issue 4, 1999, Pages 379-387

  Amiraliyev, G M ^a   Duru, Hakki ^a  

^a YUZUNCU YIL UNIVERSITY   (Turkey)

Author keywords

Difference scheme; Initial value condition; Linear ordinary differential equation; Singular perturbation; Uniform convergence

Indexed keywords

EID: 0010952169     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02458564     Document Type: Article

References (10)

1. O'Malley R E, Jr. Introduction to Singular Perturbations[M]. New York: Academic Press, 1974
2. O'Malley R E, Jr. Singular Perturbation Methods for Ordinary Differential Equations [M]. New York: Springer-Verlag, 1991
3. Neyfeh A H. Perturbation Methods[M].Wiley, 1973
4. Su Yucheng, Lin Ping. Uniform difference Scheme for a singularly perturbed linear 2nd order hyperbolic problem with zeroth order reduced equation[J]. Applied Mathematics and Mechanics (English Edition), 1990,11(4):301-313
5. Boglaev I P. Numerical integration of an initial value problem for a system with a small parameter affecting the derivative[J]. USSR Comput Math Mac Pys, 1987,27:63-75 (in Russian)
6. Doolan E P, Miller J J H, Schilders W H A. Uniform Numerical Methods for Problems with Initial and Boundary Layers[M].Dublin:Boole Press, 1980
7. Amiraliyev G M. Difference schemes on the uniform mesh for singular perturbed pseudoparabolic equations [J]. Turkish J Math, 1995,19:207-222
8. Amiraligev G M. On difference schemes for problems of the theory of dispersive waves [J]. Soviet Math Dokl, 1991,42:235-238
9. Amiraliyev G M. Difference method for the solution of one problem of the theory dispersive waves[J]. Differential Equations, 1990,26:2146-2154 (in Russian)
10. Samarski A A. Theory of Difference Schemes [M]. 2nd Ed. Moscow: "Nauka", 1983; German transl, Leibzig:Geest Portig, 1984