No Runge-Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the Averaged Vector Field (AVF) method can be interpreted as a Runge-Kutta method whose weights bi and abscissae ci represent a quadrature rule of degree at least that of the Hamiltonian. We prove that when the number of stages is minimal, the Runge-Kutta scheme...

The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting multi-derivative extension of midpoint method we have obtained a new implicit four, for numerical solution first-order differential equations. is symplectic and suitable both initial boundary value Hamiltonian pro...

When solving certain evolution type PDE such as the Schrödinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge-Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge-Kutta scheme with orders 3 and 4wit...

The wave diffraction from a box in a two-layer fluid was studied by time-domain approach. The Rankine source is used in the upper layer to establish the boundary equation. While the Rankine source and its images are adopted in the lower fluid. Through the construction of a function by velocity potentials of upper and lower velocity potentials on the internal surface, a single set of linear equa...

The present paper deals with the effects of Ohmic dissipative Casson fluid flow over a stretching sheet in the presence of aligned magnetic field. The present phenomenon also includes the interaction of thermal radiation and velocity slip. The governing boundary layer equations are transformed into a set of ordinary differential equations using the similarity transformations. The dimensionless ...

This paper presents an implementation of Multistructure PIDFLC. Modification has been made to structure of the proposed PIDFLC in order to make it acts as PDFLC, PIFLC or PIDFLC depending on two external signals. Two versions of this controller have been designed using VHDL language for FPGA implementation. A new package has been designed in VHDL code to implement trigonometric functions and fo...

The goal of this paper is focused on developing an efficient design strategy for simulating CNN arrays and hole-filling is implemented using RK step multistep methods to improve the performance of the image or handwritten character recognition. This approach is carried out by analyzing the important features of the hole-filler template and the dynamic process of CNN using well knownr RK step mu...

We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit ...