Numerical methods and applications. ([2018])

• Record Type: Book
• Further Information: Note: Edited by Guri I. Marchuk.
• Editors: Marchuk, G. I (Guriĭ Ivanovich), 1925-2013
• Contents: Cover; Half Title; Title Page; Copyright Page; Contents; 1. Iterative Methods Based on Linearization for Nonlinear Elliptic Grid Systems; 1. Preconditioning and Symmetrization of Linear Systems; 2. Two-Stage Iterative Methods for Nonlinear Systems; 3. Choice of Model Grid Operators: Optimal and Nearly Optimal Preconditioning; 4. Examples of Applications of Two-Stage Iterative Methods for Nonlinear Elliptic Problems; References; 2. How to Solve Stiff Systems of Differential Equations by Explicit Methods; 1. Problem Statement and Assumptions 2. Formulation of Four Methods Involving Explicit Difference Schemes with Time-Variable Steps3. Implicit Schemes for Linear Equations; 4. Investigation of Stability and Approximation of Explicit Difference Schemes; 5. Investigation of Stability and Approximation of Implicit Difference Schemes; 6. Some Estimates for Polynomials; 7. Determination of Parameters of Difference Equations; 8. One Realization of Stable Algorithms; 9. On Passing Boundary Layers, Estimating Quantities Cou and Ï#x84; and the DUMKA Code; 10. Cases of Stiff System Computations; References 3. On Numerical Methods of Solving the Navier-Stokes Equations in â#x80;#x9C;Velocity-Pressureâ#x80;#x9D; Variables1. Numerical Methods for Solution of the Stationary Stokes Problem; 2. Methods for Solving Nonstationary Stokes Problems; 3. Numerical Methods for Nonlinear Equations; References; 4. Stiff Systems of Ordinary Differential Equations; 1. Linear Stiff Systems; 2. A-Stability of Difference Schemes; 3. Singularly-Perturbated Systems; 4. Numerical Integration of a Singularly-Perturbated System; 5. On Regular Stiff Systems; 6. Some Applications of the Theory; 7. Slow Processes in a Nuclear Reactor 8. On the Accuracy of Eulerâ#x80;#x99;s Implicit SchemeReferences; 5. Convergence Rate Estimates of Finite-Element Methods for Second-Order Hyperbolic Equations; 1. Initial-Boundary Value Problem for Second-Order Multidimensional Hyperbolic Equations; 2. Three-Level Finite-Element Method with Weight; 3. Second-Order Accuracy A Priori Error Estimates; 4. Fractional-Order Error Estimates in Nonsmooth Data Classes; 5. The W12, h and Ch Error Estimates for the One-Dimensional Case; 6. Second-Order Hyperbolic Equations of General Form; 7. Finite-Element Method with the Splitting Operator 8. Two-Level Finite-Element Method9. Abstract Second-Order Hyperbolic Equations: Applications to Dynamic Problems of Mechanics; References; 6. Fictitious Domain Methods and Computation of Homogenized Properties of Composites with a Periodic Structure of Essentially Different Components; 1. Homogenization; 2. Fictitious Gradients Method: Perforated Composites; 3. Composites with Inclusions of a Soft Material; 4. Composites with Inclusions of Soft Materials and with Cavities; 5. On a Function Extension on a Torus; References; Index
• Publisher Details: Boca Raton, FL : CRC Press, Taylor & Francis Group
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 518; Numerical analysis; Computational Numerical Analysis; Mathematics & Statistics for Engineers; MATHEMATICS / Numerical Analysis; Electronic books
• Languages: English
• ISBNs: 9780203711200; 0203711203; 9781351359702; 1351359703; 9781351359696
• Related ISBNs: 1138105821; 9781138105829; 9781138561007; 135135969X
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.