3 edition of **The iterative solution of elliptic difference equations.** found in the catalog.

- 106 Want to read
- 39 Currently reading

Published
**1957**
by Courant Institute of Mathematical Sciences, New York University in New York
.

Written in English

The Physical Object | |
---|---|

Pagination | 37 p. |

Number of Pages | 37 |

ID Numbers | |

Open Library | OL20424632M |

Elliptic Differential Equations: Theory and Numerical Treatment (Springer Series in Computational Mathematics Book 18) - Kindle edition by Hackbusch, Wolfgang. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Elliptic Differential Equations: Theory and Numerical Treatment (Springer Manufacturer: Springer. Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse symmetric and non-symmetric linear systems: conjugate-gradients, preconditioners. Prerequisite: either AMATH , AMATH /MATH , or permission of instructor. Offered jointly with MATH

Solution of Elliptic Equation | Laplace Equation | Problem#2 | Complete Concept - Duration: /15 Numerical Methods for Partial Differential Equati views. Iterative Solution of Elliptic Finite-Difference Equations Singularities in Elliptic Equations IV. Practical Problems in Partial Differential Equations Elliptic Equations in Nuclear Reactor Problems Solution by Characteristics of the Equations of One-Dimensional Unsteady Flow Finite-Difference Methods for One-Dimensional.

Substantially revised second edition covers linear and nonlinear parabolic equations, analysis of errors, first and second order hyperbolic equations, elliptic boundary value problems, systematic iterative methods, consistent orderings of matrices, large linear systems. The general theory Methods for solving non-linear difference schemes Example Solutions of Elliptic Grid Equations Methods for constructing implicit iterative schemes Systems of elliptic equations Methods for solving elliptic equations in irregular regions Methods for Solving Elliptic Equationsin Curvilinear.

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The applications of finite difference methods have been revised and contain examples involving the The iterative solution of elliptic difference equations. book of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics.

Emphasis throughout is on clear exposition of the construction and solution of difference by: Cite this paper as: Saad Y., Sameh A. () Iterative methods for the solution of elliptic difference equations on multiprocessors. In: Brauer W. et al. (eds) Conpar Cited by: 6. Wachspress, E.

L., Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, New Jersey, zbMATH Google Scholar [3] Young, D. M., Iterative Solution of Large Linear Systems, Academic Press, New York, zbMATH Google ScholarCited by: 3.

The first part of this paper considers the effect on the solution of the difference equations from the general self-adjoint elliptic second order partial differential equation of a periodicity condition in the x-direction. There are different effects according to whether n, the number of mesh lengths in this direction, is odd or even, but for Laplace’s equation the asymptotic rates of Cited by: ITERATIVE METHODS FOR SOLVING PARTIAL DIFFERENCE EQUATIONS OF ELLIPTIC TYPE BY DAVID YOUNGO 1.

Introduction. In the numerical solution by finite differences of bound-ary value problems involving elliptic partial differential equations, one is led to consider linear systems of high order of the form N. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J.

Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data In this Chapter, the finite difference method for the solution of the Elliptic partial differential equations is discussed.

Basic Approximations Assume that three points on separated by a distance, as shown in Figure and consider the value of the function at these three points. ITERATIVE METHODS FOR NONLINEAR ELLIPTIC EQUATIONS 3 One iteration in (8) is cheap since only the action of Anot A 1 is needed.

But the method is not recommend to use for large size problems since the step size should be small enough (in the size of h2 even for the linear problem) and thus it takes large iteration steps to converge to the.

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, we have selected for coverage mostlyalgorithms and methods of analysis which.

Numerical Method Elliptic Equations- Solution of Laplace's Equation by Liebmann's iteration - Duration: Prakasam S 1, views. The Map of Mathematics - Duration: Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods.

The solution of PDEs can be very challenging, depending on the type of equation, the number of. With elliptic equations in the plane, the boundary conditions are specified round a closed curve, and the finite difference schemes then lead to a large set of linear algebraic equations for the.

The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation.

Difference approximations for Laplace's equation in two dimensions. A scheme based on the integral method. Difference schemes based on interpolation.

The iterative solution of linear equations. General remarks on the convergence of iterative methods. Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems.

It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. We consider elliptic partial differential equations in d variables and their discretisation in a product grid I = d j=1Ij: The solution of the discrete system is a grid function, which can.

() Numerical solution of non-separable elliptic equations by the iterative application of FFT methods. International Journal of Computer Mathematics() Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems.

Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ. 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. Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence.

The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to /5(3).

We study iterative methods for solving linear systems arising from two-cyclic discretizations of non-self-adjoint two-dimensional elliptic partial differential equations.

The methods consist of applying one step of cyclic reduction, resulting in a “reduced system” of half the order of the original discrete problem, combined with a. Diﬀerential equations are called partial diﬀerential equations (pde) or or-dinary diﬀerential equations (ode) according to whether or not they contain partial derivatives.

The order of a diﬀerential equation is the highest order derivative occurring. A solution (or particular solution) of a diﬀerential equa.solution of the three types of partial differential equations, namely: elliptic, parabolic, and hyperbolic equations. This method was introduced by engineers in the late 50’s and early 60’s for the numerical solution of partial differential equations in structural engineering (elasticity equations, plate equations, and .This means elliptic equations are well suited to describe equilibrium states, where any discontinuities have already been smoothed out.

For instance, we can obtain Laplace's equation from the heat equation u t = Δ u {\displaystyle u_{t}=\Delta u} by setting u t = 0 {\displaystyle u_{t}=0}.