scholarly journals Application of approximate matrix factorization to high order linearly implicit Runge–Kutta methods

2015 ◽  
Vol 286 ◽  
pp. 196-210 ◽  
Author(s):  
Hong Zhang ◽  
Adrian Sandu ◽  
Paul Tranquilli
Keyword(s):  
Matrix Factorization ◽  
High Order ◽  
Runge Kutta ◽  
Approximate Matrix Factorization

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

Continuous extensions to high order runge-kutta methods

1997 ◽  
Vol 65 (3-4) ◽  
pp. 273-291 ◽  
Author(s):  
G. Papageorgiou ◽  
Ch. Tsitouras
Keyword(s):  
High Order ◽  
Runge Kutta

scholarly journals On Runge-Kutta processes of high order

1964 ◽  
Vol 4 (2) ◽  
pp. 179-194 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
High Order ◽  
Runge Kutta ◽  
Image Position

An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.

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