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# The Method of Fractional Steps: The Solution of Problems of Mathematical Physics in Several Variables by N.N. Yanenko (Paperback, 2012)

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## About this product

### Key Features

- Author(s)N.N. Yanenko
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Date of Publication04/01/2012
- Language(s)English
- FormatPaperback
- ISBN-103642651100
- ISBN-139783642651106
- GenreMathematics

### Publication Data

- Place of PublicationBerlin
- Country of PublicationGermany
- ImprintSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Content NoteVIII, 160 p.

### Dimensions

- Weight270 g
- Width155 mm
- Height235 mm
- Pagination160

### Credits

- Translated byM. Holt

### Editorial Details

- Edition StatementSoftcover reprint of the original 1st ed. 1971

### Description

- Table Of Contents1. Uniform schemes.- 1.1 The class of problems under investigation. The Cauchy problem in Banach space.- 1.2 Uniform schemes.- 1.3 Examples.- 1.4 The method of factorization (sweep).- 1.5 The method of matrix factorization.- 2. Simple schemes in fractional steps for the integration of parabolic equations.- 2.1 The scheme of longitudinal-transverse sweep.- 2.2 The scheme of stabilizing corrections.- 2.3 The splitting scheme for the equation of heat conduction without a mixed derivative (orthogonal system of coordinates).- 2.4 The splitting scheme for the equation of heat conduction with a mixed derivative (arbitrary system of coordinates).- 2.5 The scheme of factorization of a difference operator.- 2.6 The scheme of approximate factorization of operators.- 2.7 The predictor-corrector scheme.- 2.8 Some remarks regarding schemes with fractional steps.- 2.9 Boundary conditions in the method of fractional steps for the heat conduction equation.- 3. Application of the method of fractional steps to hyperbolic equations.- 3.1 The simplest schemes for one-dimensional hyperbolic equations.- 3.2 Uniform implicit schemes for equations of hyperbolic type.- 3.3 Implicit schemes for hyperbolic equations in several dimensions.- 3.4 The splitting scheme of running computation.- 3.5 Method of approximate factorization for the wave equation...- 3.6 The method of splitting and majorant schemes.- 4. Application of the method of fractional steps to boundary value problems for Laplace's and Poisson's equations.- 4.1 The relation between steady and unsteady problems.- 4.2 The integration schemes of unsteady problems and iterative schemes.- 4.3 Iterative schemes for Laplace's equation in two dimensions S.- 4.4 Iterative schemes for Laplace's equation in three dimensions.- 4.5 Iterative schemes for elliptic equations.- 4.6 Schemes with variable steps.- 4.7 Iterative schemes based on integration schemes for hyperbolic equations.- 4.8 Solution of the boundary value problem for Poisson's equation.- 4.9 Iterative schemes with averaging.- 4.10 Reduction of schemes of incomplete approximation to schemes of complete approximation.- 5. Boundary value problems in the theory of elasticity.- 5.1 The equation of elastic equilibrium and elastic vibrations.- 5.2 Boundary value problems in the theory of elasticity.- 5.3 The integration scheme for the unsteady equations of elasticity.- 5.4 Iterative schemes of solution of boundary value problems for the biharmonic equation.- 5.5 Iterative schemes for the system of equations of elastic displacements.- 5.6 Boundary conditions in problems of elasticity.- 6. Schemes of higher accuracy.- 6.1 Uniform schemes of higher accuracy.- 6.2 Factorized schemes of higher accuracy for the equation of heat conduction.- 6.3 Solution of Dirichlet's problem with the use of the schemes of higher accuracy.- 7. Integro-differential, integral, and algebraic equations.- 7.1 Equations of kinetics.- 7.2 Algebraic equations.- 8. Some problems of hydrodynamics.- 8.1 Potential flow past a contour.- 8.2 Potential flow of an incompressible heavy liquid with a free boundary (spillway problem).- 8.3 The flow of a viscous liquid.- 8.4 The method of channel flows.- 8.5 The predictor-corrector method (method of correctors).- 8.6 The equations of meteorology.- 9. General definitions.- 9.1 General formulation of the method of splitting. Validity of the method as determined by the elimination principle in the commutative case.- 9.2 Validity of the method of splitting in the non-commutative case.- 9.3 The method of approximate factorization of an operator.- 9.4 The method of stabilizing corrections.- 9.5 The method of approximation corrections.- 9.6 The method of establishing the steady state.- 10. The method of weak approximation and the construction of the solution of the Cauchy problem in Banach space.- 10.1 Examples.- 10.2 A weak approximation for a system of differential equations.- 10.3 Convergence theorems.- References.

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