Exponential Runge–Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge–Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method. For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This all...

In this work we consider Symplectic Runge Kutta Nyström methods with five stages. A new fourth algebraic order method with phase-lag order eight is presented. Also the symplectic Runge Kutta Nyström of Calvo and Sanz Serna with five stages and fourth order is modified to produce a phase-fitted method. We apply the new methods on several Hamiltonian systems and on the computation of the eigenval...

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Power demand forecasting is a significant factor in the planning and economic and secure operation of modern power system. This research work has compared different forecasting techniques and opted to find out better technique in context of power generation, which varies rapidly from time to time. The dataset has been generated from yearly demand of electricity of Bangladesh for last five years...

In this paper, an Adaptive Neuro-Fuzzy Inference System (ANFIS) method based on the Artificial Neural Network (ANN) is applied to design an Inverse Kinematic based controller forthe inverse kinematical control of SCORBOT-ER V Plus. The proposed ANFIS controller combines the advantages of a fuzzy controller as well as the quick response and adaptability nature of an Artificial Neural Network (AN...

This paper presents a PID-like adaptive neuro-fuzzy inference system (ANFIS) controller that can be trained by the global-best harmony search (GHS) technique to control nonlinear systems. Instead of the hybrid learning methods that are widely used in the literature to train the ANFIS structure, the GHS technique alone is used to train the ANFIS as a feedback controller, and hence, the necessity...

In this paper a fully explicit, stabilized projection method called the Runge–Kutta–Chebyshev (RKC) projection method is presented for the solution of incompressible Navier–Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step. An additional projection on the time derivative of the velocity is perfo...

We analyze a quasi-Monte Carlo method to solve the initial-value problem for a system of differential equations y′(t) = f(t, y(t)). The function f is smooth in y and we suppose that f and D1 yf are of bounded variation in t and that D2 yf is bounded in a neighborhood of the graph of the solution. The method is akin to the second order Heun method of the Runge-Kutta family. It uses a quasi-Monte...

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...

There is an increasing interest in modeling groundwater contamination, particularly geogenic contaminant, on a large scale both from the researcher’s as well as policy maker’s point of view. However, modeling large scale groundwater contamination is very challenging due to the incomplete understanding of geochemical and hydrological processes in the aquifer. Despite the incomplete understanding...