Last edited by Vudokazahn

Saturday, May 16, 2020 | History

3 edition of **On the parallel solution of parabolic equations** found in the catalog.

On the parallel solution of parabolic equations

E. J. Gallopoulos

- 333 Want to read
- 19 Currently reading

Published
**1989**
by NASA Ames Research Center, Research Institute for Advanced Computer Science, National Technical Information Service, distributor in [Moffett Field, Calif.], [Springfield, Va
.

Written in English

- Approximation.,
- Chebyshev approximation.,
- Computation.,
- Linear equations.,
- Pade approximation.,
- Parabolic differential equations.,
- Parallel processing (Computers)

**Edition Notes**

Statement | E. Gallopoulos, Y. Saad. |

Series | RIACS technical report -- 89-19., NASA contractor report -- CR-180363., NASA contractor report -- NASA CR-180363. |

Contributions | Saad, Y., Research Institute for Advanced Computer Science (U.S.), Ames Research Center. |

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

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL16131192M |

Methods for solving parabolic partial differential equations on the basis of a computational algorithm. For the solution of a parabolic partial differential equation numerical approximation methods are often used, using a high speed computer for the computation. The grid . §3. Solution of boundary value problems by Rothe's method. The Cauchy problem 39 §4. The fundamental solution of a linear parabolic equation. The Green' s function. The method of integral equations for the solution of boundary value problems 63 §5. Generalized solutions of boundary value problems. The unique-ness theorem. Some auxiliary Cited by:

Purchase Numerical Solutions of Three Classes of Nonlinear Parabolic Integro-Differential Equations - 1st Edition. Print Book & E-Book. ISBN , Parallel lines are straight lines that extend to infinity without touching at any point. Perpendicular lines cross each other at a degree angle. Both sets of lines are important for many geometric proofs, so it is important to recognize them graphically and algebraically. You must know the structure of a.

This book is the first to present the application of parabolic equation methods in electromagnetic wave propagation. These powerful numerical techniques have become the dominant tool for assessing clear-air and terrain effects on radiowave propagation and are growing increasingly popular for solving scattering problems. The book gives the mathematical background to parabolic equation modelling 5/5(2). @article{osti_, title = {Numerical solution of the stochastic parabolic equation with the dependent operator coefficient}, author = {Ashyralyev, Allaberen and Department of Mathematics, ITTU, Ashgabat and Okur, Ulker}, abstractNote = {In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent.

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ON THE PARALLEL SOLUTION OF PARABOLIC EQUATIONS E. GALLOPOULOS Center for Supercomputing Research and Development University of Illinois at Urbana-Champaign Urbana, Illinois [email protected], edu Y.

SAAD RIACS, Mail Stop _ NASA Ames Research Center Moffet Field, California 9_ saadCriacs, edu ABSTRACT. Get this from a library. On the parallel solution of parabolic equations. [E J Gallopoulos; Y Saad; Research Institute for Advanced Computer Science (U.S.); Ames Research Center.].

Some of the methods designed for the numerical solution of differential equations and which present an efficient implementation within a parallel environment are briefly surveyed.

Included among these are: the Domain Decomposition and Multigrid hyper-algorithms, the Piecewise Parabolic method, the spectral (frequency) approach, some strategies Author: Carlos A.

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The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. Efficient Solution of Parabolic Equations by Krylov Approximation Methods E. Gallopoulos* and Y. Saad* Abstract Inthis paper we take a new look at numerical techniques for solving parabolic equations by the method of lines.

The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple File Size: 1MB. Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type.

The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. Numerical Analysis of Differential Equations Series solution by separation of variables: in special cases an ana-lytic representation of the (exact) solution may be constructed using the technique ofseparation of variables.

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Parabolic PDEs are used to describe a wide variety of time-dependent phenomena, including heat conduction, particle diffusion, and pricing of derivative investment instruments. Contents 1 Definition 2 Solution 3 Backward parabolic equation 4 Examples 5 See also 6 References Definition Edit To define.

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Use MathJax to format equations. Example Consider two systems of two equations in two unknowns: u+v =2 u+v =2 u+v = u+v = Solution: u =1,v=1 u =0,v=2 This example demonstrates that the change of the ﬁfth digit of one right-hand side gives totally diﬀerent solution.

Analyze now a solution of a system of linear equations Ax = b where A ∈ n×n File Size: KB. Chapter 1 contains the basic introduction to parabolic equations (existence, uniqueness, well-posedness) and to the ﬁnite diﬀerence schemes which the book is all about. Two sections deal with the solution of (almost) tridiagonal lin-ear systems of equations, and the Lax-Richtmyer equivalence theorem is .Get this from a library!

Domain decomposition methods for the numerical solution of partial differential equations. [Tarek P A Mathew] -- "Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type.

They include iterative.The book is split into diffusion (parabolic), hyperbolic, and elliptic type lessons, and discusses how to solve these using a variety of methods (including integral transforms, Fourier transforms, separation of variables).

The book even goes into numeric methods. It is an amazing bargain for 10 dollars.