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An explicit-implicit method for a class of time-dependent partial differential equations

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
9
Issue
2
Identifiers
DOI: 10.1016/0168-9274(92)90012-3
Keywords
  • Partial Differential Equations
  • Explicit-Implicit Methods
  • Method Of Lines
  • Tridiagonal Systems
  • Incomplete Cyclic Reduction
  • Stability
  • Vector And Parallel Computers
  • Domain Decomposition.
Disciplines
  • Mathematics

Abstract

Abstract For the integration of partial differential equations, we distinguish explicit and implicit methods. In this paper, we consider an explicit-implicit method, which follows from the truncation of the solution process of a fully implicit method. Such a method is of interest because not only better vectorizing properties can be obtained by increasing the explicit part, but the method also fits well in a domain-decomposition approach. In this paper, we focus on the feasibility of such methods by studying their stability and accuracy properties. Nevertheless, we also did some experiments on vectorcomputers to show that for a sufficient degree of explicitness our method is more efficient than fully implicit methods.

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