We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation...

We deal with an initial-boundary value problem for the generalized time-dependent Schrödinger equation with variable coefficients in an unbounded n–dimensional parallelepiped (n ≥ 1). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transparent boundary conditions is considered. We present its stability properties and derive new error e...

A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options. At each timestep a set of one dimensional partial integral differential equations (PIDEs) is solved and the solution of each PIDE is updated using semi-Lagrangian timestepping. Crank-Nicolson and second order backward differencing timestepping schemes are studied. Monotonicity and stability results ...

This paper addresses the construction of absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential or with a cubic nonlinearity. Semi-discrete time schemes, based on Crank-Nicolson approximations, are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbin...

In a recent study of sign-balanced, labelled posets, Stanley introduced a new integral partition statistic srank(π) = O(π)−O(π′), where O(π) denotes the number of odd parts of the partition π and π′ is the conjugate of π. In a forthcoming paper, Andrews proved the following refinement of Ramanujan’s partition congruence mod 5: p0(5n+ 4) ≡ p2(5n+ 4) ≡ 0 (mod 5), p(n) = p0(n) + p2(n), where pi(n)...

Pre-participation screening is very important for prescribing and practising exercise safely. The aim of this study was to investigate both ratings of perceived exertion (RPE) and blood pressure responses in two different types of exercises with matching duration and indirectly determined working heart rate (HR). Participants were 23 male students, who were generally healthy but sedentary. The ...

Manipulating seat configuration (i.e., seat tube angle, seat height and pelvic orientation) alters the bicycle-rider geometry, which influences lower extremity muscle kinematics and ultimately muscle force and power generation during pedaling. Previous studies have sought to identify the optimal configuration, but isolating the effects of specific variables on rider performance from the confoun...

During lower limb exercise, blood flow through the resting upper limbs exhibits a change characterized by increased anterograde flow during systole, but also large increases in retrograde diastolic flow. One explanation for the retrograde flow is that increased sympathetic nervous system (SNS) tone and concomitant increased peripheral resistance generate a rebound during diastole. To examine wh...

The temperature distribution due to a rotating or dithering Gaussian laser beam on a finite body is obtained numerically. The authors apply various techniques to solve the nonhomogeneous heat equation in different spatial dimensions. The authors’ approach includes the Crank-Nicolson method, the Fast Fourier Transform (FFT) method and the commercial software COMSOL. It is found that the maximum ...

The objectives of the present study are to investigate thermal radiation of a viscous incompressible unsteady chemically reacting and hydromagnetic fluid flow past an impulsively started vertical plate with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy...