1. Third-order methods for first-order hyperbolic partial differential equations. Author Cheema, T. A., Taj, M. S. A., and Twizell, E. H. Subjects *PARTIAL differential equations, *HYPERBOLIC differential equations, *FINITE differences, *NUMERICAL analysis, *ALGORITHMS Abstract In this paper numerical methods for solving first-order hyperbolic partial differential equations are developed. These methods are developed by approximating the first-order spatial derivative by third-order finite-difference approximations and a matrix exponential function by a third-order rational approximation having distinct real poles. Then parallel algorithms are developed and tested on a sequential computer for an advection equation with constant coefficient and a non-linear problem. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2004 Full Text View/download PDF
2. Numerical computation of a damped slewing beam with tip mass. Author Chen, Guanrong, Chen, Zhongying, and Xu, Yuesheng Subjects *ALGORITHMS, *FINITE element method, *NUMERICAL analysis, *PARTIAL differential equations, *HERMITE polynomials Abstract This paper describes an analytical model for a beam system, based on a modified Timoshenko theory, where the beam is pinned to a hub driven by an actuator at one end and is subject to a heavy load at the other end. A new efficient computational algorithm is then proposed for solving the higher-order non-canonical partial differential equation model, which is developed based on the generalized difference method. This allows a suitable selection of different trial and test spaces, so as to improve the computational efficiency while preserving the high convergence rate of the standard finite element method. With the trial space of cubic Hermite finite elements and the test space of piecewise linear functions, the computational scheme reduces to a semi-discretized or even fully discretized computational algorithm. A numerical simulation result is included to visualize the theoretical modelling and computational results. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 1999 Full Text View/download PDF