A FAST NUMERICAL METHOD FOR THE SOURCE RECONSTRUCTION IN THE COAGULATION-FRAGMENTATION EQUATION

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Abstract

A fast numerical method is proposed for the problem of restoring the source function in the Smoluchowski coagulation-fragmentation equation. The proposed method is based on the earlier work with a more detailed description of the transition from the coagulation-fragmentation equation to the final system of variational equations and the iterative process. Exploitation of the low-rank matrices has been introduced into this process to reduce the computational complexity of each iteration. The proposed methodology allows speeding up the calculations by thousands of times without losing the accuracy of the original approach.

About the authors

R. T Zaks

Marchuk Institute of Computational Mathematics RAS; Lomonosov Moscow State University

Email: zaks.robert@bk.ru
Moscow, Russia

S. A Matveev

Lomonosov Moscow State University; Marchuk Institute of Computational Mathematics RAS

Email: matseralex@gmail.com
Moscow, Russia

V. P Shutyaev

Marchuk Institute of Computational Mathematics RAS

Moscow, Russia

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