A Third-Order Direct Integrators of Runge-Kutta Type for Special Third-Order Ordinary and Delay Differential Equations

Embedded explicit Runge – Kutta type methods for directly solving special third order differential equations

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Embedded explicit Runge-Kutta type methods for directly solving special third order differential equations y'''=f(x, y)

In this paper three pairs of embedded Runge–Kutta type methods for directly solving special third order ordinary differential equations (ODEs) of the form denoted as RKD methods are presented. The first is the RKD4(3) pair which is third order embedded in fourth-order method has the property first same as last (FSAL) whereby the last row of the coefficient matrix is equal to the vector output. ...

Third-order Composite Runge Kutta Method for Solving Fuzzy Differential Equations

In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examp...

On Oscillation Criteria for Third Order Nonlinear Delay Differential Equations

In this paper we are concerned with the oscillation of third order nonlinear delay differential equations of the form ( r2 (t) ( r1 (t)x′ )′)′ + p (t)x′ + q (t) f (x (g (t))) = 0. We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.