New Third Order Explicit Runde-Kutta Method with Equal Nodes

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...

High Order Explicit Two - Step Runge - Kutta

In this paper we study a class of explicit pseudo two-step Runge-Kutta methods (EPTRK methods) with additional weights v. These methods are especially designed for parallel computers. We study s-stage methods with local stage order s and local step order s + 2 and derive a suucient condition for global convergence order s+2 for xed step sizes. Numerical experiments with 4-and 5-stage methods sh...

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

Order Barriers for Continuous Explicit Runge - Kutta Methods

In this paper we deal with continuous numerical methods for solving initial value problems for ordinary differential equations, the need for which occurs frequently in applications. Whereas most of the commonly used multistep methods provide continuous extensions by means of an interpolant which is available without making extra function evaluations, this is not always the case for one-step met...

Eighth-order Explicit Symplectic Runge-kutta-nystrr Om Integrators

We consider the solution of Hamiltonian dynamical systems by constructing eighth-order explicit symplectic Runge-Kutta-Nystrr om integrators. The application of high-order integrators may be important in areas such as in astronomy. They require large number of function evaluations, which make them computationally expensive and easily susceptible to errors. The integrators developed in this pape...