Efficient higher order single step methods for parabolic problems. I

Authors:
James H. Bramble and Peter H. Sammon

Journal:
Math. Comp. **35** (1980), 655-677

MSC:
Primary 65N30; Secondary 65M15

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572848-X

MathSciNet review:
572848

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Abstract: Some efficient, high order methods are discussed for approximating the solution of an initial boundary value problem for a homogeneous parabolic equation with time dependent coefficients. The methods are based on Galerkin-type approximations in the spacial variables and single step methods in the time variable. The equations defining the time-stepping procedure are solved only approximately, however. A preconditioned iterative technique is used for this purpose. The resulting algorithm is shown to produce optimal order approximations using only the order of work required by the single step method applied to the parabolic problem with time independent coefficients.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572848-X

Keywords:
Parabolic equations,
Galerkin methods,
higher order methods

Article copyright:
© Copyright 1980
American Mathematical Society