2 edition of **Iterative splitting methods for differential equations** found in the catalog.

Iterative splitting methods for differential equations

Juergen Geiser

- 122 Want to read
- 39 Currently reading

Published
**2011**
by Taylor & Francis in Boca Raton
.

Written in English

- Evolution equations,
- Numerical solutions,
- Iterative methods (Mathematics)

**Edition Notes**

Includes bibliographical references and index.

Statement | Juergen Geiser |

Series | Chapman & Hall/CRC numerical analysis and scientific computation series |

Classifications | |
---|---|

LC Classifications | QA377.3 .G45 2011 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL25149880M |

ISBN 10 | 9781439869826 |

LC Control Number | 2011026633 |

Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters. Symmetry, an international, peer-reviewed Open Access journal. Dear Colleagues, Splitting methods have been applied to partial and stochastic differential equations for many years and provide the advantage of decomposing differential equations into simpler solvable sub-differential equations.

INTRODUCTION TO DIRECT AND ITERATIVE METHOD. Many important practical problems give rise to systems of linear equations written as the matrix equation. Ax = c, where A is a given n A— nnonsingular matrix and c is an n-dimensional vector; the. problem is to find an n . The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good Cited by:

We consider in this section one of the simplest iterative methods: Jacobi’s method. Although Jacobi’s method is not a viable method for most problems, it provides a convenient starting point for our discussion of iterative methods. It will also be useful as a subsidiary method by: 3. Gad E, Nakhla M, Achar R and Zhou Y () A-stable and L-stable high-order integration methods for solving stiff differential equations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, , (), Online publication date: 1-Sep

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Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave by: Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources.

It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave cturer: Chapman and Hall/CRC.

Book Description. Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources.

It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources.

It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.

We present novel iterative splitting methods to solve integrodifferential equations. Such integrodifferential equations are applied, for example, in scattering problems of plasma simulations. linear algebra, and the central ideas of direct methods for the numerical solution of dense linear systems as described in standard texts such as [7], [],or[].

Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a ﬁnite-dimensional setting File Size: KB. CHAPTER 5. ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS Convergence of Iterative Methods Recall that iterative methods for solving a linear system Ax = b (with A invertible) consists in ﬁnding some ma-trix B and some vector c,suchthatI B is invertible, andtheuniquesolutionxeofAx = bisequaltotheunique solution eu of u = Bu+ Size: KB.

iterative methods for linear systems have made good progress in scientiﬁc an d engi- neering disciplines. This is due in great part to the increased complexity and size of. system of differential equations which the coefficients of the operators M and N satisfy.

These differential equations may be of use in actually computing these coefficients. Machine methods. One of our main interests is the application of iterative processes to mathematical machines, in particular to continuous devices.

Chapter 1. Introduction. The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial di erential equation (PDE) or system of PDEs inde- pendent of type, spatial dimension or form of Size: 1MB.

ITERATIVE OPERATOR SPLITTING METHODS FOR DIFFERENTIAL EQUATIONS: PROOFTECHNIQUES AND APPLICATIONS JURGEN GEISER¨ ∗ Abstract. In this paper we describe an iterative operator-splitting method for bounded oper-ators.

Our contribution is a novel iterative method that can be applied as a splitting method to ordinary and partial diﬀerential. Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations.

It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems. For the simplification, we apply two standard iterative splitting schemes to the first order differential equations.

The first iterative process is and the second iterative process is where is the known split approximation at the time level. The split approximation at the time level is defined : Jürgen Geiser. We decompose these higher order differential equations into simpler first order differential equations.

The fast iterative schemes are applied to these simpler differential equations of the first order. These numerical schemes, based on iterative splitting methods, are stable and by: 1. The multiscale iterative splitting method (MISM) decomposes the problem into scale-dependent equations, e.g., micro-and macro-equations; then it defines some coupling operators, e.g., interpolation.

Iterative splitting schemes are based on recursive integral formulations and embed numerical integration methods for dealing with time dependence; see . The work is outlined as follows: In Section 2, we present the iterative splitting method. The accuracy and stability analysis is studied in Section by: 1.

Iterative splitting methods for differential equations. [Juergen Geiser] MethodsIterative Splitting Method Consistency Analysis of the Iterative Splitting MethodStability Analysis of the Iterative Splitting Method for Bounded OperatorsDecomposition Methods for Partial Differential EquationsIterative Schemes for Unbounded.

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel Iterative-based splitting methods that efficiently use computational and memory focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.

Model problems -- 2. Iterative decomposition of ordinary differential equations -- 3. Decomposition methods for partial differential equations -- 4. Computation of the iterative splitting methods: algorithmic part -- 5. Extensions of iterative splitting schemes -- 6.

Numerical experiments -- 7. Summary and perspectives -- 8. Large systems of ordinary, partial, or stochastic differential equations as well as integral equations can be treated by splitting techniques that decompose the problem, which involves dividing large operators into smaller sub-operators and then reducing the computational time and obtaining additional benefits.

Here, we employ the iterative operator splitting method as described in Geiser's book "Iterative Splitting Methods for Differential Equations" (). .Basic iterative methods (splitting methods, Jacobi, Gauss-Seidel, SOR) Chebyshev iterative method and matrix polynomials Krylov subspace methods (conjugate gradient method, GMRES, etc.) Projection method framework Related ideas for large-scale eigenvalue problems Methods based on biorthogonalization (if there is time).

Title: Iterative solution of differential equations. Authors: Paolo Amore, Hakan Ciftci, Francisco M. Fernandez (Submitted on 29 Sep ) Abstract: We discuss alternative iteration methods for differential equations.

We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.