Parallel algorithms of linear systems and initial value problems

Abstract

Abstract : This work is concerned with the study and implementation of parallel algorithms for solution of linear system and initial value ordinary differential equations on MIMD machine. In Chapter 1, we discuss the available types of parallel computers, showing the need for higher performance and describe a summary of Ada language. In Chapter 2, we present a survey of parallel algorithms for solving a system of linear equations. In Chapter 3, a summary of basic material is given, together with the recent parallel methods on the numerical solution of intial value problems. Chapter 4 gives a full description of two parallel algorithms to solve a system of linear equations together with the theoretical and actual costs. In Chapter 5, we introduce three types of parallel second-order variable block length methods for solution of initial value problems; a stability analysis shows that all the methods are stable, while method three and four retain satisfactory properties in a parallel environment. We also give the experimental and the theoretical Finally, Chapter 6 contains a description of an algorithm for solving initial value problems using a new fourth order method. costs. All the computational results we present in this work are carried out on Sequent Balance 8000.