Two-level finite difference scheme of improved accuracy order for time-dependent problems of mathematical physics |
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Authors: | P N Vabishchevich |
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Institution: | (1) Engineering Faculty, Department of Mechanical Engineering, Kocaeli University, Kocaeli, 41380, Turkey |
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Abstract: | In the theory of finite difference schemes, the most complete results concerning the accuracy of approximate solutions are
obtained for two- and three-level finite difference schemes that converge with the first and second order with respect to
time. When the Cauchy problem is numerically solved for a system of ordinary differential equations, higher order methods
are often used. Using a model problem for a parabolic equation as an example, general requirements for the selection of the
finite difference approximation with respect to time are discussed. In addition to the unconditional stability requirements,
extra performance criteria for finite difference schemes are presented and the concept of SM stability is introduced. Issues
concerning the computational implementation of schemes having higher approximation orders are discussed. From the general
point of view, various classes of finite difference schemes for time-dependent problems of mathematical physics are analyzed. |
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