The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numeri...

This paper presents a quadrature injection locked frequency divider (ILFD) employing tunable active inductors (TAIs), which are used is to extend the locking range and to reduce die area. The CMOS ILFD is based on a new quadrature voltage-controlled oscillator (VCO) with cross-coupled switching pairs and TAI-C tanks, and was fabricated in the 0.18-μm 1P6M CMOS technology. The divide-by-2 LC-tan...

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an isogeometric discretization approach to partial differential equations on surfaces using subdivision methodology. Elliptic equations with the Laplace-Beltra...

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...

The subject of this work is the application of fully discrete Galerkin finite element methods to initial-boundary value problems for linear partial integro-differential equations of parabolic type. We investigate numerical schemes based on the Padé discretization with respect to time and associated with certain quadrature formulas to approximate the integral term. A preliminary error estimate i...

Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction o...

We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a...

Analogous to multiple-symbol differential detection of quadrature phase-shift keying (QPSK), a multiple-bit differential detection scheme is described for offset QPSK that also exhibits continuous improvement in performance with an increasing observation interval. Being derived from maximum-likelihood (ML) considerations, the proposed scheme is purported to be the most power-efficient scheme fo...

Abstract   In this paper elastoplastic buckling of rectangular plates with different boundary conditions are investigated. Differential governing equations of plate are obtained on the basis of general loading and according to deformation theory (DT) of plasticity. Various loading conditions contain uniaxial, biaxial and shear are studied. The employed material is AL7075T6 which is usually used...