This project provides an implementation of the Runge-Kutta method of order 4 for numerical integration of systems of differential equations. The Runge-Kutta method is a widely used numerical technique ...

This report provides a detailed examination of Runge-Kutta methods, which are widely used numerical techniques for solving differential equations. The objective is to offer a deep understanding of ...

Abstract: High-order uncertain differential equations are used to model differentiable uncertain systems with high-order differentials, and how to solve the high-order uncertain differential equations ...

Abstract: Ordinary differential equations are solved numerically using number of methods. In this paper, an analysis of finding out the solution of n-th order differential equations has been done ...

This paper mainly presents Euler method and fourth-order Runge Kutta Method (RK4) for solving initial value problems (IVP) for ordinary differential equations (ODE). The two proposed methods are quite ...

The purpose of this study is the design of efficient methods for the solution of an ordinary differential system of equations arising from the semidiscretization of a hyperbolic partial differential ...

ABSTRACT: In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic ...

Finite element methods provide a robust, mature family of discretizations for partial differential equations, as they provide rigorous theory, general geometry, and fast solvers. Modern trends in ...