Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the is solved numerically. We propose to ensure positivity other by applying Runge-Kutta integration which method weights are adapted order enforce bounds. The chosen at each step after calculating stage derivatives, a way that also pre...

A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher’s group and B-series are shown to provide a suitable framework for renormalizing a toy model of field theory, following Kreimer’s approach. Finally B-series are used to solve a class of non-linear partial differential equations.

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

We consider an abstract time-dependent, linear parabolic problem u′(t) = A(t)u(t), u(t0) = u0, where A(t) : D ⊂ X → X, t ∈ J , is a family of sectorial operators in a Banach space X with time-independent domain D. This problem is discretized in time by means of an A(θ) strongly stable Runge-Kutta method, 0 < θ < π/2. We prove that the resulting discretization is stable, under the assumption ‖(A...

In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs) and present some sufficient conditions for multi-symplecticity of PRK methods of Hamiltonian PDEs.

Adomian decomposition method, as a convenience device has been used to solve many functional equations so far. In this manuscript, we consider a system of nonlinear ordinary differential equations, which governs on general reaction in biochemistry as a theoretical problem of concentration kinetics. These system, which is known as Brusselator system has been solved by applying Adomian decomposit...

Research on parallel iterated methods based on Runge-Kutta formulas both for stii and non-stii problems has been pioneered by van der Houwen et al., for example see 8, 9, 10, 11]. Burrage and Suhartanto have adopted their ideas and generalized their work to methods based on Multistep Runge-Kutta of Radau type 2] for non-stii problems. In this paper we discuss our methods for stii problems and s...

In this paper we introduce a new class of explicit one-step methods of order 2 that can be used for solving stiff problems. This class constitutes a generalization of the two-stage explicit Runge-Kutta methods, with the property of having an A-stability region that varies during the integration in accordance with the accuracy requirements. Some numerical experiments on classical stiff problems ...

Among the most popular methods for the solution of the Initial Value Problem are the Runge–Kutta pairs of orders 5 and 4. These methods can be derived solving a system of nonlinear equations for its coefficients. For achieving this, we usually admit various simplifying assumptions. The most common of them are the so called row simplifying assumptions. Here we negligible them and present an algo...