An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 1: Theoretical Investigation

Rahrovani, Sadegh; Abrahamsson, Thomas; Modin, Klas

doi:10.1007/978-3-319-04522-1_25

Cited by 2 publications

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“…Moreover, long-term simulations are often required to detect nonlinear effects and investigate the properties of models that appear over time [4]. Therefore, it is necessary to implement parallel calculations and apply new numerical algorithms that reduce the computational costs of simulations while maintaining accuracy [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…In matrix (6), four state variables have equal feedback numbers, corresponding to step 3(2) of the algorithm. Let us calculate the number of feedbacks in cases of excluding a column of each such variable and write the result as a matrix, where the excluded variables are located in the columns and the sums in the rows Mathematics 2021, 9, x FOR PEER REVIEW 9 of 17…”

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confidence: 99%

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Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Тутуева

Butusov

2021

Mathematics

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The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

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