A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

This paper is concerned with numerical solution of the transient acoustic–structure interaction problems in three dimensions. An efficient and higher-order method is proposed with a combination of the exponential window technique and a fast and accurate boundary integral equation solver in the frequency-domain. The exponential window applied to the acoustic–structure system yields an artificial...

In this paper, we study a parabolic equation with purely nonlocal (integral) conditions. We present a numerical approximate solution by Laplace transform method. Some experimental numerical results using the proposed numerical procedure are discussed.

In the present paper the authors propose two numerical methods to approximate Hadamard transforms of the type Hp( f wβ , t) = ∫ = R f (x) (x − t)p+1 wβ (x)d x , where p is a nonnegative integer and wβ (x) = e−|x | β , β > 1, is a Freud weight. One of the procedures employed here is based on a simple tool like the “truncated” Gaussian rule conveniently modified to remove numerical cancellation a...

We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...

This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trad...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

The idea of employing the discrete Fourier transform casted as the representative cell method for the solution of multiscale problems is illustrated. Its application in combination with analytical (structural mechanics methods, Wiener-Hopf method, integral transform methods) and numerical (finite element method, higher-order theory) methods is demonstrated. Both cases of 1-D and 2-D translation...