A quasi-randomized Runge-Kutta method

Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems

We analyze explicit Runge–Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs-type. For the time discretization, we consider explicit secondand third-order Runge–Kutta schemes. We identify a general set of properties on the spatial stabilization, encompassing continuous a...

A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws

In this paper we present an a priori error estimate of the Runge-Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge-Kutta method and the finite element space is made up of piecewise polynomials of degree k ≥ 2. Quasi-optimal error estimate is obtained by energy techniques,...

Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

In this paper we present the analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method to solve scalar conservation laws, where the time discretization is the third order explicit total variation diminishing Runge–Kutta (TVDRK3) method. We use an energy technique to present the L-norm stability for scalar linear conservation laws, and obtain a priori error estimates for smooth solutions...

Méthodes de Runge-Kutta-Fehlberg

High Order Runge { Kutta Methods on Manifolds

This paper presents a family of Runge{Kutta type integration schemes of arbitrarily high order for di erential equations evolving on manifolds. We prove that any classical Runge{Kutta method can be turned into an invariant method of the same order on a general homogeneous manifold, and present a family of algorithms that are relatively simple to implement.