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27 September 2022 A numerical study for a novel super-time-stepping method with one-dimensional nonlinear parabolic equations
Huan Zhang, Hui-Jie Bai, Lin Li
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Proceedings Volume 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022); 123450B (2022) https://doi.org/10.1117/12.2649021
Event: 2022 International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 2022, Qingdao, China
Abstract
For solving nonlinear parabolic partial differential equations, some explicit methods have strict time step constraints and implicit methods have poor parallel scalability. So we propose a new explicit method for solving one-dimensional nonlinear parabolic problems. Taking advantage of its derivation mechanism, we put forward a simplified algorithm. This explicit RKL method adopts the s-stage strategy promoted by time to expand the time step, breaking the time limit of the previous explicit method in the parabolic problem, and it is easier to implement than the implicit method. Using shifted Legendre polynomials, we can intelligently obtain a scalable stable interval of the RKL method and the effective stable interval varies with s. We have designed some RKL schemes with a short recursive sequence and successfully implemented Burgers, Fisher equation, and other nonlinear problems. This fact has been verified.
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Huan Zhang, Hui-Jie Bai, and Lin Li "A numerical study for a novel super-time-stepping method with one-dimensional nonlinear parabolic equations", Proc. SPIE 12345, International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 123450B (27 September 2022); https://doi.org/10.1117/12.2649021
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KEYWORDS
Numerical analysis
Partial differential equations
Error analysis
Algorithms
Ordinary differential equations
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