Accession Number : ADA295663

Title :   The Large Discretization Step Method for Time-Dependent Partial Differential Equations.

Descriptive Note : Contractor rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Haras, Zigo ; Ta'asan, Shlomo

PDF Url : ADA295663

Report Date : APR 1995

Pagination or Media Count : 53

Abstract : A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS, in short) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes. (AN)

Descriptors :   *APPROXIMATION(MATHEMATICS), *NUMERICAL INTEGRATION, *PARTIAL DIFFERENTIAL EQUATIONS, *HEURISTIC METHODS, MATHEMATICAL MODELS, ALGORITHMS, COMPUTATIONS, HIGH RATE, TIME DEPENDENCE, TWO DIMENSIONAL, ACCELERATION, GRIDS, ACCURACY, THREE DIMENSIONAL, FINITE DIFFERENCE THEORY, SOLUTIONS(GENERAL), DISCRETE DISTRIBUTION, OPERATORS(MATHEMATICS), EULER EQUATIONS, NUMERICAL METHODS AND PROCEDURES, NONLINEAR ALGEBRAIC EQUATIONS, FOURIER ANALYSIS, CORRECTIONS, LINEAR ALGEBRAIC EQUATIONS.

Subject Categories : Numerical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE