An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear sys...

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

Using the abstract framework of [9] we analyze a residual a posteriori error estimator for space-time finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and...

This paper is concerned with transparent boundary conditions for the one dimensional time–dependent Schrödinger equation. They are used to restrict the original PDE problem that is posed on an unbounded domain onto a finite interval in order to make this problem feasible for numerical simulations. The main focus of this article is on the appropriate discretization of such transparent boundary c...

OBJECTIVES Uncoupled cycling cranks are designed to remove the ability of one leg to assist the other during the cycling action. It has been suggested that training with this type of crank can increase mechanical efficiency. However, whether these improvements can confer performance enhancement in already well-trained cyclists has not been reported. METHOD Fourteen well-trained cyclists (13 m...

Since conventional crank-driven compressor had many difficulties to increase efficiency due to mechanical loss, new kind of compressor has been paid much of attention by the compressor manufacturers. The free piston compressor mechanism has been one of those kinds. The compressor manufacturers developed an energy efficient free piston linear resonance compressor for a household refrigerator. In...

In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting shape of the crank generating function. We fit this function in a more general family of inverse theta functions which play a key role in physics.

Suppression of soleus H-reflex amplitude in stationary legs is seen during rhythmic arm cycling. We examined the influence of various arm-cycling parameters on this interlimb reflex modulation to determine the origin of the effect. We previously showed the suppression to be graded with the frequency of arm cycling but not largely influenced by changes in peripheral input associated with crank l...