Algorithms known as ``particle'' methods, whose characteristic feature is the discretization technique when the set of discrete objects is introduced, which are model ``particles'' considered as some mesh of moving nodes, are becoming more and more widespread in mathematical modelling. Until recently, particle methods have mainly been developed as an alternative to classical numerical methods for solving problems in plasma physics. As a result, no specialized monographs on this subject had been available. The aim of this book is to fill the gap in literature on this subject and deals with combined Lagrangian-Eulerian schemes of the ``particle-in-cell'' type, the most widespread among particle methods. The authors describe a universal approach to the construction of such algorithms.

The approach is based on splitting the initial problem by which the auxiliary problem with a hyperbolic (divergent) operator is separated. After special discretization of the solution, such a splitting naturally leads to the well-known schemes of ``particle-in-cell'' methods. Examples of calculations in this book give the reader an idea of the capabilities of particle-in-cell methods, their requirements to computers, and the degree of precision that can be achieved. This book is primarily intended for specialists in calculations, who want to get a general idea of numerical particle-in-cell methods and the sphere of their applications. As a methodological guide, it will be of interest to undergraduate and postgraduate students, mathematicians and physicists specializing in mathematical modelling.

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