Factorized SM-stable two-level schemes |
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Authors: | P N Vabishchevich |
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Institution: | 1.Institute of Mathematical Modeling,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | Additional requirements for unconditionally stable schemes were formulated by analyzing higher order accurate difference schemes
in time as applied to boundary value problems for second-order parabolic equations. These requirements concern the inheritance
of the basic properties of the differential problem and lead to the concept of an SM-stable difference scheme. An earlier
distinguished class of SM-stable schemes consists of the schemes based on various Padé approximations. The computer implementation
of such higher order accurate schemes deserves special consideration because certain matrix polynomials must be inverted at
each new time level. Factorized SM-stable difference schemes are constructed that can be interpreted as diagonally implicit
Runge-Kutta methods. |
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Keywords: | |
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