This paper describes an effort to develop timestepping methods for partial differential equations that can overcome the difficulties that existing methods have with stiffness of the system of ordinary differential equations that results from spatial discretization. Stiffness is caused by the contrasting behavior of coupled components of the solution, and makes “one-size-fits-all” polynomial and...

Abstract Maximum likelihood estimation of the parameters stochastic differential equations commonly used in finance requires numerical approximation their transitional probability density functions. This article undertakes a comparative study accuracy Hermite polynomial expansion approximations for univariate diffusions and checks how existing methods responds to increasing order approximation....

Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions of high degree ...

In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre- and post-buckled rectangular plates for the first time. This is an answer to an existing need to develope a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element...

This paper presents a wideband 2 13-bit in-phase/ quadrature-phase (I/Q) RF digital-to-analog converter-based alldigital modulator realized in 65-nm CMOS. The isolation between I and Q paths is guaranteed employing 25% duty-cycle differential quadrature clocks. With a 1.3-V supply and an on-chip power combiner, the digital I/Q transmitter provides more than 21-dBm RF output power within a frequ...

I t is a pleasure to o er this essay for Mathematics Today as a record of my Summer Lecture on 29 June 2011 at the Royal Society. Polynomials are as basic a topic as any in mathematics, and for numerical mathematicians like me, they are the starting point of numerical methods that in some cases go back centuries, like quadrature formulae for numerical integration and Newton iterations for findi...

Quasi-Monte Carlo (QMC) rules 1/N ∑N−1 n=0 f(ynA) can be used to approximate integrals of the form ∫ [0,1]s f(yA) dy, where A is a matrix and y is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications fr...

Mahalanobis distance may be used as a measure of the disparity between an individual's profile of scores and the average profile of a population of controls. The degree to which the individual's profile is unusual can then be equated to the proportion of the population who would have a larger Mahalanobis distance than the individual. Several estimators of this proportion are examined. These inc...