The numerical solution of parabolic Volterra integro-differential equations on unbounded spatial domains

Applied Numerical Mathematics

Volumn 55, Issue 1, 2005, Pages 83-99

  Han, Houde ^a   Zhu, Liang ^a   Brunner, Hermann ^b   Ma, Jingtang ^c  

^a TSINGHUA UNIVERSITY   (China)

^b MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

^c HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Artificial boundary conditions; Numerical time stepping; Parabolic Volterra integro differential equations; Unbounded spatial domain

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DIFFUSION; NUMERICAL METHODS; ONE DIMENSIONAL; PROBLEM SOLVING;

ARTIFICIAL BOUNDARY CONDITIONS; NUMERICAL TIME-STEPPING; PARABOLIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS; UNBOUNDED SPATIAL DOMAIN;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 21844440830     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.10.010     Document Type: Article

References (12)

1. H. Brunner, and P.J. van der Houwen The Numerical Solution of Volterra Equations CWI Monographs vol. 3 1986 North-Holland Amsterdam
2. C. Chen, and T. Shih Finite Element Methods for Integrodifferential Equations Series on Applied Math. vol. 9 1998 World Scientific Singapore
3. E. Hairer, and G. Wanner Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems second ed. 1996 Springer-Verlag Berlin
4. H. Han, and Zh. Huang A class of artificial boundary conditions for heat equation in unbounded domains Comput. Math. Appl. 43 2002 889 900
5. H. Han, and Zh. Huang Exact and approximating boundary conditions for the parabolic problems on unbounded domains Comput. Math. Appl. 44 2002 655 666
6. H. Han, and X. Wu Approximation of infinite boundary condition and its application to finite element methods J. Comput. Math. 3 1985 179 192
7. H. Han, and X. Wu The mixed element method for Stokes equations on unbounded domains J. Systems Sci. Math. Sci. 5 1985 121 132
8. H. Han, and X. Wu The approximation of the exact boundary condition at an artificial boundary for linear elastic equations and its application Math. Comp. 59 1992 21 27
9. P. Henrici Applied and Computational Complex Analysis, vol. 1 1974 Wiley New York
10. H.H. Rosenbrock Some general implicit processes for the numerical solution of differential equations Comput. J. 5 1963 329 331
11. Ph. Souplet Blow-up in nonlocal reaction-diffusion equations SIAM J. Math. Anal. 29 1998 1301 1334
12. E.G. Yanik, and G. Fairweather Finite element methods for parabolic partial integro-differential equations Nonlinear Anal. 12 1988 785 809