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Monday, August 3, 2020 | History

2 edition of Parallelism in the numerical integration of initial value problems found in the catalog.

Parallelism in the numerical integration of initial value problems

B. P. Sommeijer

# Parallelism in the numerical integration of initial value problems

## by B. P. Sommeijer

Written in English

Subjects:
• Differential equations -- Numerical solutions.,
• Initial value problems -- Numerical solutions.,
• Parallel processing (Electronic computers)

• Edition Notes

The Physical Object ID Numbers Statement B.P. Sommeijer. Series CWI tract -- 99., CWI tract -- 99. Contributions Houwen, P. J. van der 1939-, Couzy, W. Pagination v, 195 p. ; Number of Pages 195 Open Library OL14696154M ISBN 10 9061964318

This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue. MEBDF; Referenced in 75 articles large sparse systems of stiff initial value efficient algorithm for the numerical integration large sparse systems of stiff initial value ordinary differential equations and differential-algebraic equations algorithm is illustrated by application to several problems of practical interest and its performance.

() Second derivative of high-order accuracy methods for the numerical integration of stiff initial value problems. Afrika Matematika , () The efficiency of second derivative multistep methods for the numerical integration of stiff by: Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc. ( views) Introduction to the Numerical Integration of PDEs by B. Piette - University of Durham,

Final-value ODEs: Stable numerical integration and its application to parallel circuit analysis Abstract: While solving initial-value ODEs is the de facto approach to time-domain circuit simulation, the opposite act, solving final-value ODEs, has been neglected for a long time. techniques presented in my textbook. This really is a tutorial (not a reference), meant to be read and used in parallel with the textbook. For this reason, I have structured the tutorial to have the same chapter and sections titles as the book. However, the purpose of the sections of this document is not to re-explain theFile Size: KB.

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### Parallelism in the numerical integration of initial value problems by B. P. Sommeijer Download PDF EPUB FB2

Get this from a library. Parallelism in the numerical integration of initial value problems. [B P Sommeijer; P J Parallelism in the numerical integration of initial value problems book der Houwen; W Couzy]. Parallelism in the numerical integration of initial value problems () Pagina-navigatie: Main; Save publication.

Save as MODS; Export to Mendeley; Save as EndNoteCited by: 8. Parallelism in the numerical integration of initial value problems () Pagina-navigatie: Main; Save publication. Save as MODS; Export to Mendeley; Save as EndNote; Export to RefWorks; Title: Parallelism in the numerical integration of initial value problems: Author: B.P.

Sommeijer (Ben) Date issued: Access: Closed Access Cited by: 8. For the parallel integration of stiff initial value problems (IVPs) three main approaches can be distinguished: approaches based on “parallelism across the problem”, on “parallelism across the method” and on “parallelism across the steps”.

The first type of parallelism does not require special integration methods can be exploited within any Cited by: 6. As a first step toward developing a parallel algorithm for the numerical solution of the initial-value problem, let us consider how we might widen the computation front.

The predictor-corrector method of numerical integration provides a means for doing this. In its usual form this method of numerical integration is just as. () Parallel algorithms for solving nonlinear two-point boundary-value problems which arise in optimal control.

Journal of Optimization Theory and Applications() A Survey of Parallel Algorithms in Numerical Linear by: Publisher Summary.

This chapter discusses the numerical treatment of singular/discontinuous initial value problems. The mathematical formulation of physical phenomena in simulation, electrical engineering, control theory, and economics often leads to an initial value problem in which there is a pole in the solution or a discontinuous low order derivative.

Parallel Numerical Integration 1 Numerical Integration an application of domain decomposition quad double arithmetic Romberg integration 2 Parallel Numerical Integration using OpenMP using the Intel TBB: parallel_reduce Introduction to Supercomputing (MCS ) Parallel Numerical Integration L 21 September 6 / 30File Size: KB.

Numerical Integration of First Order ODEs (1) The generic form of a ﬁrst order ODE is dy dt = f(t,y); y(0) = y 0 where the right hand side f(t,y) is any single-valued function of t and y. The approximate numerical solution is obtained at discrete values of t t j = t 0 +jh where h is the “stepsize” NMM: Integration of ODEs page 7File Size: KB.

For a given value of $$y_0$$ and each fixed $$x$$, the integral on the right can be evaluated by numerical methods. An alternate procedure is to apply the numerical integration procedures discussed in Chapter 3 directly to the initial value problem Equation \ref{eq}.

For the numerical solution of initial value problems a general procedure to determine global integration methods is derived and studied.

They are collocation methods which can be easily. Some details of highly parallel implementations of high-precision numerical integration are given in [8]. In one recent application of these methods, the authors addressed Problem. Purchase Numerical Methods for Initial Value Problems in Ordinary Differential Equations - 1st Edition.

Print Book & E-Book. ISBNBook Edition: 1. The amount of parallelism for solving initial value problems such as ODEs is often quite limited, but by exploiting some characteristics of the application area where these problems are solved, the amount of parallelism can be increased.

We focus on solving ODEs for rolling bearing dynamics simulation, which is computationally by: 8. IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on AugustIt focuses on the numerical solution of the initial value problem, where is a vector of rate functions r 1, which depend on intensive thermodynamical variables of which temperature T and concentrations c 1.

(moles/unit volume) are the most important. The chapter explains the initial value problem. The chapter discusses a few special features. all the constants of integration are specified at the same place, they are called initial values and the problem of finding a solution is called an initial value problem.

In addition, to find a numerical solution, the range of the independent variable for which the solution is desired must also be specified.

This range must contain the initial File Size: KB. From Wikipedia, the free encyclopedia Parareal is a parallel algorithm from numerical analysis and used for the solution of initial value problems. It was introduced in by Lions, Maday and Turinici.

Since then, it has become one of the most widely studied parallel-in-time integration methods. In view of the challenges from exascale computing systems, numerical methods for initial value problems which can provide concurrency in temporal direction are being studied. Parareal is a relatively well known example of such a parallel-in-time integration method, but early ideas go back into the s.

Analysis. ideas associated with constructing numerical solutions to initial-value problems that are beyond the scope of this text. Indeed, a full discussion of the application of numerical methods to differential equations is best left for a future course in numerical analysis.

Euler’s Method. 6 Numerical Integration Basic Concepts In this chapter we are going to explore various ways for approximating the integral of a function over a given domain. There are various reasons as of why such approximations can be useful.

First, not every function can be analytically integrated. Second, even if aFile Size: KB.Numerical Integration of Partial Differential Equations (PDEs) • Introduction to PDEs. •• SemiSemi--analytic methods to solve analytic methods to solve PDEsPDEs. •• Introduction to Finite uction to Finite Differences.

•• Stationary Problems, Elliptic Stationary Problems, Elliptic PDEsPDEs.Parallel Programming (PP) book, Chapters12 Data parallelism (Max. DOP) scale well with size of problem e.g. to improve throughput of a number of instances of the same problem Divide problem is into smaller parallel problems of the same type as the original larger problem then combine results Fundamental or Common e.g.

2D Grid O(n2.