IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE - Qays Younis Mahmmod; Akram S. Mohammed; Zeyas M. Abdullah (Tikrit Journal of Pure Science, 2023)
The aim of the study is to explain the numerical solutions of the one dimensional (1-D) of heat by using method of lines (MOLs). In the (MOLs) the derivative is firstly transformed to equivalent 5 point central finite differences methods (FDM) that is also transformed to the ordinary differential equations (ODEs). The produced (ODEs) systems are solved by the well-known techniques method of ODEs such as the 4th Runge - Kutta method and Runge - Kutta Fehlberg. And since of the conversion of the second derivative to the equivalent of the 5 points FDM which led to an increase in the size of the system equations ODEs, and thus increased we have improved the performance of these (MOLs) techniques by  introduce parallel processing to speed up the solution of the produced ODE systems. The developed parallel technique, are suitable for running on MIMD (Multiple Instruction Stream, Multiple Data Stream) computers.