An Explicit Finite Difference Solver by Parameter Estimation

  • S. K. Dey
  • C. Dey
Conference paper


Explicit finite difference schemes are possibly the simplest methods to solve initial value problems. The main drawback, however, is that in order to maintain stability of computation, step size must be small. This often increases computer run time, especailly when steady-state solutions are needed. In ref. [1], the second author combined a predictor which is an explicit finite difference scheme with a one-step corrector and solved Burgers’ equation given in section 7. The step sizes were chosen such that the stability criterion for the predictor alone was violated. The corrector required estimation of a filtering parameter such that stability properties may be maintained.


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  1. 1.
    Dey, S.K. and Dey, C. (1983) An Explicit Predictor-Corrector Solver with Applications to Burgers’ Equation. NADA Tech. Memo. 84402.Google Scholar
  2. 2.
    Dey, C. and Dey, S.K. (1983) Explicit Finite Difference Predictor and Convex Corrector with Applications to Hyper bolic Partial Differential Equations. Computer and Math. with Applications. 9, 1 : 549–557.CrossRefzbMATHGoogle Scholar
  3. 3.
    Lomax, H. (1983) Private Communication. NASA-Ames Research Center.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • S. K. Dey
    • 1
  • C. Dey
    • 2
  1. 1.Mathematics DepartmentEastern Illinois UniversityCharlestonUSA
  2. 2.7th GraderCharleston Jr. High SchoolCharlestonUSA

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