Stability Analysis of 4-Stage Stochastic Runge-Kutta Method (SRK4) and Specific Stochastic Runge-Kutta Method (SRKS1.5) for Stochastic Differential Equations

2019 ◽  
pp. 187-194
Author(s):  
Noor Amalina Nisa Ariffin ◽  
Norhayati Rosli ◽  
Abdul Rahman Mohd Kasim
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Explicit order 3/2 Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion

2019 ◽  
Vol 17 (1) ◽  
pp. 1515-1525
Author(s):  
Yazid Alhojilan
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Taylor Expansion ◽  
Transport Theory ◽  
Numerical Solutions ◽  
Optimal Transport ◽  
Stochastic Integrals ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract This paper aims to present a new pathwise approximation method, which gives approximate solutions of order $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions. The new method, which assumes the diffusion matrix non-degeneracy, employs the Runge-Kutta method and uses the Itô-Taylor expansion, but the generating of the approximation of the expansion is carried out as a whole rather than individual terms. The new idea we applied in this paper is to replace the iterated stochastic integrals Iα by random variables, so implementing this scheme does not require the computation of the iterated stochastic integrals Iα. Then, using a coupling which can be found by a technique from optimal transport theory would give a good approximation in a mean square. The results of implementing this new scheme by MATLAB confirms the validity of the method.

scholarly journals Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations

2020 ◽  
pp. 134-140
Author(s):  
M. O. Ogunniran ◽  
O. A. Tayo ◽  
Y. Haruna ◽  
A. F. Adebisi
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Classical Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Mind

Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.

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