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• W2103446321 abstract "It is well known that methods for solving semidiscretized parabolic partial differential equations based on the second-order diagonal [1/1] Padé approximation (the Crank–Nicolson or trapezoidal method) can produce poor numerical results when a time discretization is imposed with steps that are “too large” relative to the spatial discretization. A monotonicity property is established for all diagonal Padé approximants from which it is shown that corresponding higher-order methods suffer a similar time step restriction as the [1/1] Padé. Next, various high-order methods based on subdiagonal Padé approximations are presented which, through a partial fraction expansion, are no more complicated to implement than the first-order implicit Euler method based on the [0/1] Padé approximation; moreover, the resulting algorithms are free of a time step restriction intrinsic to those based on diagonal Padé approximations. Numerical results confirm this when various test problems from the literature are implemented on a Multiple Instruction Multiple Data (MIMD) machine such as an Alliant FX/8. © 1993 John Wiley & Sons, Inc." @default.
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• W2103446321 date "1993-03-01" @default.
• W2103446321 modified "2023-09-27" @default.
• W2103446321 title "On parallel algorithms for semidiscretized parabolic partial differential equations based on subdiagonal Padé approximations" @default.
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• W2103446321 doi "https://doi.org/10.1002/num.1690090202" @default.
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