Optimized high-order splitting methods for some classes of parabolic equation
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Other documents of the author: Blanes, Sergio; Casas, Fernando; Chartier, Philippe; Murua, Ander
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Optimized high-order splitting methods for some classes of parabolic equationDate
2013Publisher
American Mathematical SocietyISSN
0025-5718; 1088-6842Bibliographic citation
BLANES, Sergio, et al. Optimized high-order splitting methods for some classes of parabolic equations. Mathematics of Computation, 2013, vol. 82, no 283, p. 1559-1576.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Weareconcernedwiththenumericalsolutionobtainedbysplitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative ... [+]
Weareconcernedwiththenumericalsolutionobtainedbysplitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It has been demonstrated that this second-order barrier can be overcome by using splitting methods with complex-valued coefficients (with positive real parts). In this way, methods of orders 3 to 14 by using the Suzuki–Yoshida triple (and quadruple) jump composition procedure have been explicitly built. Here we reconsider this technique and show that it is inherently bounded to order 14 and clearly sub-optimal with respect to error constants. As an alternative, we solve directly the algebraic equations arising from the order conditions and construct methods of orders 6 and 8 that are the most accurate ones available at present time, even when low accuracies are desired. We also show that, in the general case, 14 is not an order barrier for splitting methods with complex coefficients with positive real part by building explicitly a method of order 16 as a composition of methods of order 8. [-]
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Mathematics of Computation, 2013, vol. 82, no 283Rights
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