‎Second derivative general linear methods (SGLMs) as an extension‎ ‎of general linear methods (GLMs) have been introduced to improve‎ ‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ ‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ ‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually Runge--Kutta stability conditions‎. ‎In this p...

In this paper, a numerical technique is applied to a five variable giving up smoking fractional mathematical model. This model is based on five types of smokers, i.e. potential, occasional, heavy, temporary quitters and permanent quitters. Efficacy of Perturbation Iteration Algorithm on fractional system of differential equations is shown graphically between standard Runge-Kutta method and PIA.

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...

Abstract: In this paper Differential Transform Method (DTM) is implemented to solve some Riccati differential equations with variable co-efficients. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The results derived by this method are compared with the numerical results by Runge Kutta 4 (R...

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total...

We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is applied for two time integration techniques: fourth order low–storage explicit Runge–Kutta (LSERK4) and second order Leapfrog (LF2). The CPLTS method is applied to evolve Maxwell’s curl equations using a Discontinuous Galerkin (DG) sch...

We investigate conservative properties of Runge-Kutta methods for Hamiltonian PDEs. It is shown that multi-symplecitic Runge-Kutta methods preserve precisely norm square conservation law. Based on the study of accuracy of Runge-Kutta methods applied to ordinary and partial differential equations, we present some results on the numerical accuracy of conservation laws of energy and momentum for H...

This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...

This research demonstrates a solution for the DICE 2007 integrated assessment model in the continuous domain through the use of a Runge-Kutta sampling technique for solving differential transcendental equations. The use of a savings ratio helper constraint was not required. It is shown that the introduction of a savings ratio constraint leads to a 12% underestimation of maximum atmospheric temp...