We consider two-dimensional scattering problems, formulated as an integral equation defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency scattering problems necessitates a large number of unknowns in classical boundary element methods. In addition, the corresponding discretization matrix of the integral equation is dense. We formulate a boundary element m...

In this article, homotopy perturbation method coupled with Laplace transform and Padé 0approximants is applied on the re-formulated nonlinear oscillatory systems. Numerical results and graphical represenations explicitly reveal the complete reliability and effeicincy of the suggested algorithm.

This article studies the forced oscillatory behavior of solutions to nonlinear hyperbolic equations with functional arguments. Our main tools are the integral averaging method and a generalized Riccati technique.

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each ...

In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (...

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-or...

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...

A simple procedure for decreasing the statistical error associated with Monte Carlo integration of oscillatory functions is presented. The method uses available information about the integral of a similar oscillatory function to correlate the estimates of the positive and negative components of the integral. Numerical tests show that information guided noise reduction (IGNoR) leads to substanti...