in this paper, the numerical algorithms for solving ‘fuzzy ordinary differential equations’ are considered. a scheme based on the 4th order runge-kutta method is discussed in detail and it is followed by a complete error analysis. the algorithm is illustrated by solving some linear and nonlinear fuzzy cauchy problems.

In this work a systematic procedure is implemented in order to minimise the computational cost of the Runge–Kutta–Munthe-Kaas (RKMK) class of Lie-group solvers. The process consists of the application of a linear transformation to the stages of the method and the analysis of a graded free Lie algebra to reduce the number of commutators involved. We consider here RKMK integration methods up to o...

The Runge–Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge–Kutta time discretizations, and limiters. In this paper, we investigate using the RKDG finite element method for compressible...

We consider a special class of partitioned linearly-implicit Runge-Kutta methods for the solution of multibody systems in index 3 formulation. In contrast to implicit methods these methods require only the solution of linear systems for the algebraic variables. We study convergence and consistency of the methods and give numerical results for a special method of order 4 and comparisons.

A new explicit fourth-order six-stage Runge-Kutta scheme with low dispersion and low dissipation properties is developed. This new Runge-Kutta scheme is shown to be more efficient in terms of dispersion and dissipation properties than existing algorithms such as Runge-Kutta temporal schemes developed by Hu et al. (1996), Mead and Renaut (1999), Tselios and Simos (2005). We perform a spectral an...

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties, which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local tr...

A new type of variable coefficient Runge-Kutta-Nyström methods is proposed for solving the initial value problems of the special form y(t) = f(t, y(t)). The method is based on the exact integration of some given functions in order to solve the problem exactly when the solution is the linear combination of these functions. If this is not the case, the algebraic order (order of accuracy) of the m...

In this article, we report results of an experimental study on six iterative methods to compute the transient probabilities of large Markov models: full matrix exponentiation, forward Euler method, explicit Runge-Kutta methods of order 2 and 4 and Adams-Bashforth multi-steps methods of order 2 and 4. We suggest a simple but efficient implementation of these algorithms. We discuss how to tune th...

In this paper we consider the numerical solution of 2D systems of certain types of taxis-diiusion-reaction equations from mathematical biology. By spatial discretization these PDE systems are approximated by systems of positive, nonlinear ODEs (Method of Lines). The aim of this paper is to examine the numerical integration of these ODE systems for low to moderate accuracy by means of splitting ...

In this paper, we propose a functional fitting s-stage Runge-Kutta method which is based on the exact integration of the set of the linearly independent functions u i (t), (i = 1,. .. , s). The method is exact when the solution of the ODE can be expressed as the linear combination of u i (t), although the method has an error for general ODE. In this work we investigate the order of accuracy of ...