A Matlab package for automatically generating Runge-Kutta trees, order conditions, and truncation error coefficients

2006 ◽  
Vol 32 (2) ◽  
pp. 274-298 ◽  
Author(s):  
Frank Cameron
Keyword(s):  
Truncation Error ◽  
Order Conditions ◽  
Runge Kutta ◽  
Matlab Package ◽  
Error Coefficients

scholarly journals A DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTROM (RKN) METHOD FOR SOLVING SECOND ORDER ODES ON PARALLEL COMPUTERS

2020 ◽  
Vol 4 (3) ◽  
pp. 513-522
Author(s):  
Sunday Obomeviekome Imoni
Keyword(s):  
Truncation Error ◽  
Parallel Computers ◽  
Standard Test ◽  
Interval Of Periodicity ◽  
Second Order ◽  
Test Problems ◽  
Empty Interval ◽  
Oscillatory Solutions ◽  
Runge Kutta ◽  
Error Coefficients

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

scholarly journals Order Conditions of Stochastic Runge--Kutta Methods by B-Series

2000 ◽  
Vol 38 (5) ◽  
pp. 1626-1646 ◽  
Author(s):  
K. Burrage ◽  
P. M. Burrage
Keyword(s):  
Order Conditions ◽  
Runge Kutta
Sign in / Sign up

Export Citation Format

Share Document