Compact finite difference method for integro-differential equations

Applied Mathematics and Computation

Volumn 177, Issue 1, 2006, Pages 271-288

  Zhao, Jichao ^a   Corless, Robert M ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Compact finite difference method; Fredholm equations; High accuracy; IDE; Integro differential equations; Volterra equations

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; MATRIX ALGEBRA; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

COMPACT FINITE DIFFERENCE METHOD; FREDHOLM EQUATIONS; HIGH ACCURACY; VOLTERRA EQUATIONS;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 33744519384     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.11.007     Document Type: Article

References (13)

1. Karameta A., and Sezer M. A Taylor collocation method for the solution of linear integro-differential equations. Int. J. Comput. Math. 79 9 (2002) 987-1000
2. Liz E., and Nieto J.J. Boundary value problems for second order integro-differential equations of Fredholm type. J. Comput. Appl. Math. 72 (1996) 215-225
3. H. Yang, Numerical analysis of American options, Ph.D. Thesis, University of Alberta, 2001.
4. Styś K., and Styś T. A higher-order finite difference method for solving a system of integro-differential equations. J. Comput. Appl. Math. 126 (2000) 33-46
5. M.O. Ahmed, An exploration of compact finite difference methods for the numerical solution of PDE, Ph.D. thesis, the University of Western Ontario, 1997.
6. R. Cont, P. Tankov, E. Voltchkova, Option pricing models with jumps: integro-differential equations and inverse problems, European Congress on Computational Methods in Applied Sciences and Engineering, 24-28 July 2004, pp. 1-20.
7. Li R.H., Chen Z.Y., and Wu W. Generalized Difference Methods for Differential Equations (Numerical Analysis of Finite Volume Methods) (2000), Marcel Dekker, Inc., New York
8. Varga R.S. Matrix Iterative Analysis (2000), Springer, Berlin, New York
9. Corless R.M., and Rokicki J. The symbolic generation of finite-difference formulas. Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM) Proceedings. ICIAM/GAMM 95, Numerical Analysis, Scientific Computing, Computer Science. Hamburg, Germany: 3 July 1995-7 July 1995. In: Alefeld G., Mahrenholtz O., and Mennicken R. (Eds). ZAMM vol. 76, Suppl. (1995), Akademie-Verlag, Germany 381-382
10. R.M. Corless, J. Rokicki, J. Zhao, FINDIF, a routine for generation of finite difference formulae, Share Library package 1994, and upgraded to n dimensions for "iguana".
11. R. Natalini, M. Briani, C.L. Chioma, Finite differences schemes for integro-differential equations in financial mathematics, IAC-CNR & University, 2003.
12. Zhang T. Finite Element Methods for Evolution Integro-Differential Equations (2001), Northeastern University Press, Shenyang of China
13. Liu W. The exponential stabilization of the high dimensional linear system of thermoviscoelasticity. J. Math. Pures Appl. 77 (1998) 355-386