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

S.Dubey ¹ , S. Prajapat² , R. Verma³ , R. Jhaggar⁴

1. International Institute of Professional Studies, Devi Ahilya University, Indore, India.
2. International Institute of Professional Studies, Devi Ahilya University, Indore, India.
3. International Institute of Professional Studies, Devi Ahilya University, Indore, India.
4. International Institute of Professional Studies, Devi Ahilya University, Indore, India.

Correspondence should be addressed to: rajendra93verma@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.5 , pp.57-62, Oct-2017

CrossRef-DOI:   https://doi.org/10.26438/ijsrcse/v5i5.5762

Online published on Oct 30, 2017

Copyright © S.Dubey, S. Prajapat, R. Verma, R. Jhaggar . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

495 Views    854 Downloads    102 Downloads

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.

Key-Words / Index Term :
Differential equation, Parallel Processing, Core, SIMD, Euler’s Method, maxNumCompThreads , Execution time

References :
[1] A. Ma, "On Improving Euler Methods for Initial Value Problems", Scholar Research Library, Nigeria, ISSN 0975-508X, pp. 369-379, 2010.
[2] A. Ochoche, "Improving the Improved Modified Euler Method for Better Performance on Autonomous Initial Value Problems ", Leonardo Journal of Sciences, Nigeria, ISSN 1583-0233, Issue 12, pp. 57-66, 2008.
[3] S. P. Mondal, S. Roy and B. Das,"Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application", International Journal of Differential Equations, Vol. 2016, Article ID 8150497, 2016.
[4] M. A. Akanbi, "A Third Order Euler Method for Numerical Solution of Ordinary Differential Equation", ARPN Journal of Engineering and Applied Sciences, Nigeria, ISSN 1819-6608, Vol. 5, Issue 8, pp. 42-49, 2010.
[5] S. Fadugba, B. Ogunrinde, T. Okunlola, "Euler’s Method for Solving Initial Value Problems in Ordinary Differential Equations", The Pacific Journal of Science and Technology, Nigeria, Vol. 13, Issue 2, pp. 152-158, 2012.
[6] V. Rajaraman, “Computer Oriented Numrical Methods”, Prentice – Hall of India PHI Publications , Edition 3, pp 164-183, 2004 .
[7] R. Jaiswal, A. A. Pathan ,"Study of Numerical Analysis – Differential Equation", International Journal of Advanced Research in Computer Science and Software Engineering,Volume 5, Issue 10, pp. 709- 713,2015.
[8] A. Rajput, B. Ishwarkar, S.Kadhao, "Parallel Processing Unit with MIMD Architecture", International Journal of Advanced Research in Computer Science and Software Engineering,Volume 4, Issue 4, pp. 1055-1060, 2014..
[9] K. Soetaert, T. Petzoldt and R. W. Setzer, "Solving Differential Equations in R", The R Journal, ISSN 2073-4859, Vol. 2, Issue. 2, pp. 5-15, 2010.
[10] R. S. Kareem, ``Numerical Methods for Fractional Differential Equations", International Journal of Computer Science and Network Security, Iraq, VOL. 14, Issue. 1, pp. 42-45, 2014.
[11] S. Dubey, R. Jhaggar, R. Verma, D. Gaur, "Encryption and Decryption of Data by Genetic Algorithm", International Journal of Scientific Research in Computer Science and Engineering, Vol.5, Issue.3, pp.47-52, 2017.
[12] S.Dubey, R. Jhaggar, N. Jhariya, A. Thakur, "System for Providing News Associated with Location", International Journal of Scientific Research in Computer Science and Engineering, Vol.5, Issue.3, pp.25-29, 2017.
[13] S. Dubey, R. Jhaggar, R. Verma, D. Gaur, "Encryption and Decryption of Data by Genetic Algorithm", International Journal of Scientific Research in Computer Science and Engineering, Vol.5, Issue.3, pp.47-52, 2017.