Abstract: In this paper, the fifth order Improved Runge-Kutta method (IRK5) that uses just five function evaluations per step is developed. The method proposed here are derived with only five stages which results in lower number of function evaluations. Therefore, IRK5 has a lower computational cost than the classical fifth order Runge-Kutta method (RK5). Here, the order conditions of the metho...

We consider implicit-explicit (IMEX) Runge Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stabilitypreserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge Kutta (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space...

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 ...

Abstract. The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison...

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-order with dispersive order six and 'small' principal local truncation error terms and dissipation constant. The analysis of phase-lag, dissipatio...

An optimized explicit low-storage fourth-order Runge–Kutta algorithm is proposed in the present work for time integration. Dispersion and dissipation of the scheme are minimized in the Fourier space over a large range of frequencies for linear operators while enforcing a wide stability range. The scheme remains of order four with nonlinear operators thanks to the low-storage algorithm. Linear a...

Abstract In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourthorder 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standar...

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...

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method an...

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...