Solution of Differential Equations by Parallel Processing and Analysis of Performance Improvement

Abstract

When solving the problems based on more than two variables most of the time relative changes on the variables need to be calculated. The degree of dependency among variables and number of variable quantities make solution finding more complex. It is very obvious to get the help of differential equations. When we deal with the functions frequently changing by nature, so it is highly likely to find local maxima, local minima, slope of tangent and value of the function at given point. Finding solution is not a single process but a set of processes where some binary operations, repetitions of the operations, checking the consistency of function within the interval etc take place. Here it becomes very important that the time taken to execute the problem of differential equation must be least. Thus the needs of pipelining, parallel processing, speculative computation etc become crucial factor. So requirement of solution of differential equations become very necessary. The degree of equation, complexity of equation, no of variables etc are the parameters those play very important roles during the solution process. When this task is assigned to serial processors the time taken to solve a problem is greater than the time taken by the parallel processors to do the same task. Here in this research we are calculating the time taken by serial processors and by parallel processors too. Although entry of vector processors and array processors improved the performance very much but since performance is the subject to frequently improvement. So putting that context in mind our study has tried to minimize the time taken for solving the differential equation by dividing a big problem in small ones in such a way so that dependency for data among processors i.e. communication will be very less. Means research has tried to improve the ratio of computation over communication ratio.