Effects of multiplicative noise on the Duffing oscillator with variable coefficients and its integral of motion

2020 ◽  
Vol 31 (07) ◽  
pp. 2050095
Author(s):  
E. Urenda-Cázares ◽  
A. Gallegos ◽  
R. Jaimes-Reátegui
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Multiplicative Noise ◽  
Duffing Oscillator ◽  
Variable Coefficients ◽  
Kutta Method ◽  
Integral Of Motion ◽  
Runge Kutta Method

In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

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