Abstract—In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing ...

In computational aeroacoustics (CAA) simulations, discontinuous Galerkin space discretization (DG) in conjunction with Runge-Kutta time integration (RK), which is so called Runge-Kutta discontinuous Galerkin method (RKDG), has been an attractive alternative to the finite difference based high-order numerical approaches. However, when it comes to complex physical problems, especially the ones in...

We compare six numerical integrators' performance when simulating a regular spiking cortical neuron model whose 74-compartments are equipped with eleven membrane ion channels and Calcium dynamics. Four methods explicit two implicit; three finite difference PDE methods, Runge-Kutta one an exponential time differencing method. Three first-, commonly considered second-, fourth-order. Derivations s...

Despite the popularity of high-order explicit Runge–Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit–explicit Runge–Kutta (IMEX-RK) schemes to overcome geometry...

Based on First Same As Last (FSAL) technique, an embedded trigonometrically-fitted Two Derivative Runge-Kutta method (TDRK) for the numerical solution of first order Initial Value Problems (IVPs) is developed. Using the trigonometrically-fitting technique, an embedded 5(4) pair explicit fifth-order TDRK method with a “small” principal local truncation error coefficient is derived. The numerical...

In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced decomposition is introduced. This decomposition allows any residual occurring in the implicit equation of the implicit-step to be moved into the explicit part of the decomposition. By balancing the residual, the accuracy of the local truncation error of the time-st...

Splitting methods are a frequently used approach for the solution of large stiff initial value problems of ordinary differential equations with an additively split right-hand side function. Such systems arise, for instance, as method of lines discretizations of evolutionary partial differential equations in many applications. We consider the choice of explicit Runge-Kutta (RK) schemes in implic...