IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE
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 e...
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Tikrit University
2023-01-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/684 |
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| author | Qays Younis Mahmmod Akram S. Mohammed Zeyas M. Abdullah |
| author_facet | Qays Younis Mahmmod Akram S. Mohammed Zeyas M. Abdullah |
| author_sort | Qays Younis Mahmmod |
| collection | DOAJ |
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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.
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| format | Article |
| id | doaj-art-8a00a85b30a0445b9b9a6b6eef4d53a3 |
| institution | Matheson Library |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-8a00a85b30a0445b9b9a6b6eef4d53a32025-07-12T07:22:50ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262023-01-0123610.25130/tjps.v23i6.684IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENEQays Younis MahmmodAkram S. MohammedZeyas M. Abdullah 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. https://tjpsj.org/index.php/tjps/article/view/684parallel solutionsmethod of linesDifference Methods5FDMRunge – Kutta 4orderRunge – Kutta 5 order |
| spellingShingle | Qays Younis Mahmmod Akram S. Mohammed Zeyas M. Abdullah IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE Tikrit Journal of Pure Science parallel solutions method of lines Difference Methods 5FDM Runge – Kutta 4order Runge – Kutta 5 order |
| title | IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE |
| title_full | IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE |
| title_fullStr | IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE |
| title_full_unstemmed | IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE |
| title_short | IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE |
| title_sort | improving parallel solutions for method of lines to 1 d heat equation by using five point finite differene |
| topic | parallel solutions method of lines Difference Methods 5FDM Runge – Kutta 4order Runge – Kutta 5 order |
| url | https://tjpsj.org/index.php/tjps/article/view/684 |
| work_keys_str_mv | AT qaysyounismahmmod improvingparallelsolutionsformethodoflinesto1dheatequationbyusingfivepointfinitedifferene AT akramsmohammed improvingparallelsolutionsformethodoflinesto1dheatequationbyusingfivepointfinitedifferene AT zeyasmabdullah improvingparallelsolutionsformethodoflinesto1dheatequationbyusingfivepointfinitedifferene |