A sharp error estimate for the numerical solution of multivariate Dirichlet problem for the heat equation

Stochastic Analysis and Applications

Volumn 19, Issue 3, 2001, Pages 343-360

  Anastassiou, George A ^a   Bendikov, Alexander ^a  

^a University of Memphis   (United States)

Author keywords

Approximate solution; Average operator; Convergence with rates; Dirichlet problem continuous and discrete; First and second moduli of continuity; First exit time; Heat equation; Sharp inequality; Space time; Space time random walk; Wiener process

Indexed keywords

EID: 0035608552     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-100002015     Document Type: Article

References (7)

1. B. Büttgenbach, H. Esser, and R.S. Nessel, On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations, Numer. Funct. Anal. Optim., 12 (1991), 285-298.
2. B. Büttgenbach, H. Esser, G. Lüttgens, and R.J. Nessel, A sharp error estimate for the numerical solution of a Dirichlet problem for the Poisson equation, Jour. of Comput. and Appl. Math., 44 (1992), 331-337.
3. W. Dickmeis, R.J. Nessel, and E. Van Wickeren, Quantitative extensions of the uniform boundedness principle, Jahr. Deutsch. Math. Verein. 89 (1987), 105-134.
4. J.L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, New York, 1984.
5. H. Esser, St. J. Goebbels, G. Lüttgens, R.J. Nessel, Sharp-error bounds for the Crank-Nicolson and Saulyev difference scheme in connection with an initial boundary value problem for the inhomogeneous heat equation, to appear in Special Issue on "Concrete Analysis", "J. Computers & Mathematics with Applications", 1995.
6. K. Ito and M.P. McKean, Diffusion Processes and Their Sample Path, Springer-Verlag, Berlin, 1974.
7. F. Spitzer, Principles of Random Walk, Graduate Texts in Math., 34, Springer-Verlag, 1976.