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Anderson acceleration method of finding steady-state particle size distribution for a wide class of aggregation-fragmentation models

机译:寻找广泛聚集 - 碎片模型的稳态粒度分布的安德森加速方法

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摘要

A fast numerical method of finding steady-state distributions of particles sizes for a wide class of aggregation fragmentation models, including the models with a source of monomers is developed. The method is based on a fast evaluation scheme for large sets of non-linear Smoluchowski-type ODE with an application of the Anderson acceleration method of the fixed point iterations. In the numerical tests of the suggested approach we demonstrate that huge sets of non-linear ODE may be solved with high precision in terms of Euclidian norm of the residual in modest times with use of a regular desktop computer. We compare our numerical solutions with the known analytical results for the steady-state distributions as well as with the other fast numerical schemes and prove the high accuracy of the novel method and its significant superiority with respect to the existing fast numerical method of solution of the addressed problems. (C) 2017 Elsevier B.V. All rights reserved.
机译:开发了一种快速数值方法,用于找到各种聚集碎片模型的颗粒尺寸的稳态分布,包括具有单体来源的模型。 该方法基于大组非线性Smoluchowski型ode的快速评估方案,其应用于固定点迭代的Anderson加速方法。 在建议方法的数值测试中,我们证明,在适用于常规桌面计算机时,可以在剩余时间的欧几里德规范方面以高精度来解决大量的非线性颂歌。 我们将数字解决方案与稳态分布的已知分析结果进行比较,以及其他快速数字方案,并证明了新方法的高精度及其对现有的快速数值方法的显着优越性 解决了问题。 (c)2017 Elsevier B.v.保留所有权利。

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