Global error estimation and control in linearly-implicit parallel two-step peer W-methods
نویسندگان
چکیده
منابع مشابه
Efficient Global Error Estimation and Control in Explicit Parallel Peer Methods
Recently, Kulikov [1] presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely , a local error control implemented in such methods plays a part of global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme among those methods. In ...
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Linearly-implicit two-step peer methods are successfully applied in the numerical solution of ordinary differential and differential-algebraic equations. One of their strengths is that even highorder methods do not show order reduction in computations for stiff problems. With this property, peer methods commend themselves as time-stepping schemes in finite element calculations for timedependent...
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Two-step W-methods are linearly implicit time-stepping methods using s external stages that may be processed in parallel. Methods with order s + 1 and stage order s exist. Appropriate generalizations for the concepts of A-and L-stability are derived as well as necessary conditions for A-stability and suucient conditions for stii accuracy. We construct methods of order four where no order reduct...
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The construction of s-stage explicit parallel two-step peer methods for the solution of non-stiff initial value problems with optimal zero stability and order p = s is considered. By an additional condition superconvergence of order p = s + 1 can be achieved. Further criteria for good methods are large stability regions and small error constants. Corresponding parameter sets have been obtained ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2011
ISSN: 0377-0427
DOI: 10.1016/j.cam.2011.08.006