We present a new method, based on averaging, to simulate certain systems with multiple time scales efficiently and demonstrate its utility in the context of the shallow-water equations. We first develop the method in a simple linear setting and analytically prove its stability. This is followed by an extension to the full equations and a presentation of a computational model for it. In this pre...

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms...

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...

Biginelli-type reaction was developed by means of a three-component condensation of analdehyde, ethyl acetoacetate, urea or thiourea and nano alumina sulfonic acid (Al2O3-SO3H)(NASA) as catalyzed. It is carried out under different conditions. In all conditions, the desiredproducts are obtained in high yields after relatively short reaction times. Nevertheless, thereactions proceeded faster and ...

It has been shown that a vertex list assignment satisfying Hall's condition is sufficient for the existence of a proper list coloring if and only if every block of the graph is a clique. It is asked in [5] whether this can be extended to multicolorings. It is shown here that in general this is not the case. Introduction The notion of list coloring has its origins independently with Vizing [7] a...

We solve a class of initial boundary value problems posed in a time-dependent convex domain for the sine-Gordon equation and for its linearized version. We give an explicit integral representation of the solution by using the Fokas transform method; this representation, which has an explicit exponential x and t dependence, is obtained by solving a d-bar problem in the complex plane. This d-bar ...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...