Abstract
In this paper, diagonally implicit Runge-Kutta-Nystrom (RKN) method of high-order for the numerical solution of second order ordinary differential equations (ODE) possessing oscillatory solutions to be used on parallel computers is constructed. The method has the properties of minimized local truncation error coefficients as well as possessing non-empty interval of periodicity, thus suitable for oscillatory problems. The method was tested with standard test problems from the literature and numerical results compared with the analytical solution to show the advantage of the algorithm
Highlights
Runge-Kutta–Nystrom method is widely used for the numerical approximation of the initial value problem (IVP)
Several high-order diagonally implicit RungeKutta-Nystrom (DIRKN) methods have been proposed for the integration of the IVP (1) on one-processor computers
Parallel diagonally implicit Runge-Kutta-Nystrom (PDIRKN) method is presented for the approximation of the IVP (1)
Summary
Runge-Kutta–Nystrom method is widely used for the numerical approximation of the initial value problem (IVP). Several high-order diagonally implicit RungeKutta-Nystrom (DIRKN) methods have been proposed for the integration of the IVP (1) on one-processor computers. Parallelism across the method is to perform several function evaluations concurrently on different processors. The development of PDIRKN method for solving the IVPs associated with the special second order IVP (1) in the first category, which is parallelism across the method is investigated. Parallel diagonally implicit Runge-Kutta-Nystrom (PDIRKN) method is presented for the approximation of the IVP (1). The method has algebraic order two in two stages This means that the stages can be evaluated concurrently using two-processor machine. Construction of the new PDIRKN Method A Six stage, 3-parallel, 3-processor sixth order DIRKN method is investigated. The method has the sparsity pattern and diagraph shown in figure 1
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