Choice of strategies for extrapolation with symmetrization in the constant stepsize setting |
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| Institution: | 1. Department of Mathematics, Sultan Idris Education University, Campus Sultan Azlan Shah, Proton City, 35900 Tanjong Malim, Perak, Malaysia;2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand;1. Department of Mathematics, Harran University, 63290, Şanlıurfa, Turkey;2. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey;1. Department of Mathematics, Southeast University, Nanjing, 210096, PR China;2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan;1. Department of Industrial Engineering, Seoul National University, Seoul, 151-742, Republic of Korea;2. Department of Mathematics, Chungnam National University, Daejeon, 305-764, Republic of Korea |
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| Abstract: | Symmetrization has been shown to be efficient in solving stiff problems. In the constant stepsize setting, we study four ways of applying extrapolation with symmetrization. We observe that for stiff linear problems the symmetrized Gauss methods are more efficient than the symmetrized Lobatto IIIA methods of the same order. However, for two-dimensional nonlinear problems, the symmetrized 4-stage Lobatto IIIA method is more efficient. In all cases, we observe numerically that passive symmetrization with passive extrapolation is more efficient than active symmetrization with active extrapolation. |
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| Keywords: | Extrapolation Symmetrizers Symmetrization Gauss methods Lobatto IIIA methods and stiff problems |
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