High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems

2021 ◽  
Author(s):  
Khai Chien Lee ◽  
Norazak Senu ◽  
Ali Ahmadian ◽  
Siti Nur Iqmal Ibrahim
Keyword(s):  
High Order ◽  
Third Order ◽  
Exponentially Fitted ◽  
Runge Kutta

The modified high-order Haar wavelet scheme with Runge–Kutta method in the generalized Burgers–Fisher equation and the generalized Burgers–Huxley equation

2021 ◽  
pp. 2150419
Author(s):  
Ming Zhong ◽  
Qi-Jun Yang ◽  
Shou-Fu Tian
Keyword(s):  
High Efficiency ◽  
Haar Wavelet ◽  
High Order ◽  
Fisher Equation ◽  
Kutta Method ◽  
Third Order ◽  
Time Layer ◽  
Runge Kutta Method ◽  
Huxley Equation ◽  
Runge Kutta

In this work, we focus on the modified high-order Haar wavelet numerical method, which introduces the third-order Runge–Kutta method in the time layer to improve the original numerical format. We apply the above scheme to two types of strong nonlinear solitary wave differential equations named as the generalized Burgers–Fisher equation and the generalized Burgers–Huxley equation. Numerical experiments verify the correctness of the scheme, which improves the speed of convergence while ensuring stability. We also compare the CPU time, and conclude that our scheme has high efficiency. Compared with the traditional wavelets method, the numerical results reflect the superiority of our format.

Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order

2010 ◽  
Vol 181 (12) ◽  
pp. 2044-2056 ◽  
Author(s):  
M. Calvo ◽  
J.M. Franco ◽  
J.I. Montijano ◽  
L. Rández
Keyword(s):  
High Order ◽  
Exponentially Fitted ◽  
Runge Kutta

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
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