Parallel Second Order Runge – Kutta new method of the Geometric Mean

Alani, Mahmood Dhiya

doi:10.33899/berj.2020.165717

	Parallel Second Order Runge – Kutta new method of the Geometric Mean
College Of Basic Education Research Journal
Article 2, Volume 16, Issue 3, 2020, Pages 944-953 PDF (1.47 M)
Document Type: Research Paper
DOI: 10.33899/berj.2020.165717
Author
mahmood Dhiya alani^*
mosul university college of basic education mathematics department
Abstract
Runge - Kutta methods are one of the best methods for numerically solving (ODEs), and the search for better methods is always up to date [1]. Our concern here is with present a new method for solving Initial Value Problems (IVPs) using a mixing between techniques and formulas and obtain a new formula suitable for parallel computers, (see [2]). As we know a first step toward developing a parallel algorithm for the numerical solution of Initial Value Problems (IVPs), how we might widen the front of computation .The predictor – corrector (PC) methods of numerical integration provide a means for doing this, (see [3,4]) ."Evans Introduce a new Runge - Kutta method using the Geometric mean (GM) formula [5]" (see [6]). Here we collected these ideas and using the Implicit Runge - Kutta methods (IRK) which can be derived directly from Explicit Runge - Kutta methods (ERK) , these implicit methods “ that were derived “ , it is "the (backward) form of the explicit (forward) form [7]", to present our new parallel method which we called (PPCGM2) formula.
Keywords
Runge - Kutta methods; predictor - corrector method; the stability

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