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Second-order Approximation (second-order + approximation)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Plane SH-waves at a corrugated interface between two dissimilar perfectly conducting self-reinforced elastic half-spaces

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2006
S. K. Tomar
Abstract In this paper, we have attempted a problem of reflection and refraction of plane harmonic SH-wave at a corrugated interface between two different perfectly conducting self-reinforced elastic half-spaces. Rayleigh's method is employed to find out the expressions of reflection and refraction coefficients for first- and second-order approximation of the corrugation. The expressions of these coefficients show that they depend on the properties of half-spaces, angle of incidence, frequency of the incident wave and are strongly influenced by the corrugation of the interface. Numerical computations are performed for a particular model having special type of interface and the variation of these coefficients are depicted graphically against the angles of incidence, frequency parameter, corrugation parameter at different values of reinforcement parameters. Results of some earlier works are reduced as a particular case of this formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A Crank,Nicholson-based unconditionally stable time-domain algorithm for 2D and 3D problems

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2007
Xin Xie
Abstract It has been shown that both ADI-FDTD and CN-FDTD are unconditionally stable. While the ADI is a second-order approximation, CN is only in the first order. However, analytical expressions reveal that the CN-FDTD has much smaller truncation errors and is more accurate than the ADI-FDTD. Nonetheless, it is more difficult to implement the CN than the ADI, especially for 3D problems. In this paper, we present an unconditionally stable time-domain method, CNRG-TD, which is based upon the Crank,Nicholson scheme and implemented with the Ritz,Galerkin procedure. We provide a physically meaningful stability proof, without resorting to tedious symbolic derivations. Numerical examples of the new method demonstrate high precision and high efficiency. In a 2D capacitance problem, we have enlarged the time step, ,t, 400 times of the CFL limit, yet preserved good accuracy. In the 3D antenna case, we use the time step, ,t, 7.6 times larger that that of the ADI-FDTD i.e., more than 38 times of the CFL limit, with excellent agreement of the benchmark solution. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 261,265, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22101 [source]

Azimuthally symmetric theory of gravitation , I. On the perihelion precession of planetary orbits

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2010
G. G. Nyambuya
ABSTRACT From a purely non-general relativistic standpoint, we solve the empty space Poisson equation (,2,= 0) for an azimuthally symmetric setting (i.e. for a spinning gravitational system like the Sun). We seek the general solution of the form ,=,(r, ,). This general solution is constrained such that in the zeroth-order approximation it reduces to Newton's well-known inverse square law of gravitation. For this general solution, it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body. We show that to second-order approximation, this azimuthally symmetric gravitational field is capable of explaining at least two things: (i) the observed perihelion shift of solar planets; (ii) the fact that the mean Earth,Sun distance must be increasing (this resonates with the observations of two independent groups of astronomers, who have measured that the mean Earth,Sun distance must be increasing at a rate between about 7.0 ± 0.2 m century,1 and 15.0 ± 0.3 m cy,1). In principle, we are able to explain this result as a consequence of the loss of orbital angular momentum; this loss of orbital angular momentum is a direct prediction of the theory. Further, we show that the theory is able to explain at a satisfactory level the observed secular increase in the Earth year (1.70 ± 0.05 ms yr,1). Furthermore, we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least 8.00 ± 2.00 s cy,1. [source]

A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditions

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2006
Wenyuan Liao
Abstract In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction-diffusion equations is fourth-order accurate in both the temporal and spatial dimensions. We also prove that the standard second-order approximation to zero Neumann boundary conditions provides fourth-order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source]