Parallel Methods for Initial Value Problems
نویسنده
چکیده
As scientiic technology becomes increasingly more sophisticated, the production of more data and/or the modelling of more complex systems requires computers with ever-increasing computational power. In order to cope with this situation numerical algorithms have to be developed which allow the distribution of both data and code segments over large numbers of processors with the hope that problems that were insoluble in a sequential environment because of either (or both) accuracy and size constraints can now be solved in a parallel environment. This paper will present a review of recently developed techniques in the area of parallel numerical methods for Initial Value Problems. It will focus mainly on two diierent approaches-parallelism across time and parallelism across space but will also consider special techniques developed for certain classes of problems.
منابع مشابه
Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems
In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...
متن کاملTrigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems
In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...
متن کاملParallelizing Assignment Problem with DNA Strands
Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...
متن کاملSolving Some Initial-Boundary Value Problems Including Non-classical Cases of Heat Equation By Spectral and Countour Integral Methods
In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...
متن کاملThe symmetric two-step P-stable nonlinear predictor-corrector methods for the numerical solution of second order initial value problems
In this paper, we propose a modification of the second order method introduced in [Q. Li and X. Y. Wu, A two-step explicit $P$-stable method for solving second order initial value problems, textit{Appl. Math. Comput.} {138} (2003), no. 2-3, 435--442] for the numerical solution of IVPs for second order ODEs. The numerical results obtained by the new method for some...
متن کاملA Parallel Overlapping Time-Domain Decomposition Method for ODEs
We introduce an overlapping time-domain decomposition for linear initial-value 7 problems which gives rise to an efficient solution method for parallel computers without 8 resorting to the frequency domain. This parallel method exploits the fact that homogeneous 9 initial-value problems can be integrated much faster than inhomogeneous problems by using 10 an efficient Arnoldi approximation for ...
متن کامل