On Error Bounds of Finite Difference Approximations to Partial Differential Equations—Temporal Behavior and Rate of Convergence

Authors:
Saul Abarbanel;Adi Ditkowski;Bertil Gustafsson
Affiliations:
School of Mathematical Sciences, Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel;Division of Applied Mathematics, Brown University, Providence, RI 02912. adit@cfm.brown.edu;Department of Scientific Computing, Uppsala University, S-751 04 Uppsala, Sweden
Venue:
Journal of Scientific Computing
Year:
2000

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Abstract

This paper considers a family of spatially semi-discrete approximations, including boundary treatments, to hyperbolic and parabolic equations. We derive the dependence of the error-bounds on time as well as on mesh size.