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Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.

Initial value problems. --- Boundary value problems. --- Differential operators. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Operators, Differential --- Differential equations --- Operator theory --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Problems, Initial value --- Boundary value problems --- Iterative Methods. --- Operator Splitting. --- Regularized Additive Schemes. --- Summarized Approximation. --- Transition Operator Approximations. --- Two-Component Splitting. --- Vector Additive Schemes.

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Mathematics

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This book discusses questions of numerical solutions of applied problems on parallel computing systems. Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In the development of up-to-date applied software, this feature of computers must be taken into account for the maximum efficient usage of their resources. In constructing computational algorithms, we should separate relatively independent subproblems in order to solve them on a single computing node.

Parallel processing (Electronic computers) --- Computer algorithms --- Mathematics --- Math --- Science --- Algorithms --- High performance computing --- Multiprocessors --- Parallel programming (Computer science) --- Supercomputers --- Data processing

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Computer. Automation