ISSN:
1572-9044
Keywords:
parabolic equations
;
method of lines
;
rational approximations
;
parallel algorithms
;
65L05
;
65M05
;
65Y05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Time dependent problems in Partial Differential Equations (PDEs) are often solved by the Method Of Lines (MOL). For linear parabolic PDEs, the exact solution of the resulting system of first order Ordinary Differential Equations (ODEs) satisfies a recurrence relation involving the matrix exponential function. In this paper, we consider the development of a fourth order rational approximant to the matrix exponential function possessing real and distinct poles which, consequently, readily admits a partial fraction expansion, thereby allowing the distribution of the work in solving the corresponding linear algebraic systems in essentially Backward Euler-like solves on concurrent processors. The resulting parallel algorithm possesses appropriate stability properties, and is implemented on various parabolic PDEs from the literature including the forced heat equation and the advection-diffusion equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02127713
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