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A Finite Difference Parallel Method for Solving Parabolic Equations

Author: YangDanDan
Tutor: LiuBo
School: Jilin University
Course: Computational Mathematics
Keywords: Parallel computing Difference equation JGS iterative method Saul'yev non- symmetrical format Stability Truncation error
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 53
Quote: 1
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Abstract


In this paper, the parabolic equation constructed a new parallel computing format first introduced the structure of elliptic equations the JGS iterative sequence , then the iterative solution of the elliptic equations is transformed into a parallel algorithm for solving the parabolic equation finite difference , prove to know it is a stable condition . solving parabolic equations thus designed a new parallel format , is in the same odd time layer , the left boundary point classical explicit asymmetric format within a point of the use of a Saul'yev , right boundary points using the classical implicit ; classical implicit in the the next even layer left margin point , interior point another Saul'yev the asymmetric format right boundary point using the classical explicit so this format at the border point of explicit and implicit alternating interior point the two kinds Saul'yev asymmetric format alternating prove that it is absolutely stable , its truncation error reached O ( ( ? ) h2 ) results by the elliptic equations JGS iteration sequence directly transform into the parabolic equation finite difference compared to the parallel format , is satisfactory . Finally, the results of numerical experiments are also consistent with the theoretical analysis .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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