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Original Articles

A SHARP ERROR ESTIMATE FOR THE NUMERICAL SOLUTION OF MULTIVARIATE DIRICHLET PROBLEM FOR THE HEAT EQUATION

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Pages 343-360 | Published online: 01 Sep 2006

REFERENCES

  • Büttgenbach , B. , Esser , H. and Nessel , R. S. 1991 . 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 : 285 – 298 .
  • Büttgenbach , B. , Esser , H. , Lüttgens , G. and Nessel , R. J. 1992 . A sharp error estimate for the numerical solution of a Dirichlet problem for the Poisson equation . Jour. of Comput. and Appl. Math. , 44 : 331 – 337 .
  • Dickmeis , W. , Nessel , R. J. and Van Wickeren , E. 1987 . Quantitative extensions of the uniform boundedness principle . Jahr. Deutsch. Math. Verein. , 89 : 105 – 134 .
  • Doob , J. L. 1984 . Classical Potential Theory and its Probabilistic Counterpart New York : Springer-Verlag .
  • Esser , H. , Goebbels , St. J. , Lüttgens , G. and Nessel , R. J. 1995 . 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” .
  • Ito , K. and McKean , M. P. 1974 . Diffusion Processes and Their Sample Path Berlin : Springer-Verlag .
  • Spitzer , F. 1976 . Principles of Random Walk , Graduate Texts in Math., 34 Springer-Verlag .

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