The constant K has the same meaning as above. 1CAS = Computer Algebra System. 2The interval [0, 2π] is for convenience only. Everything we say can easily be extended to an arbitrary interval [a, b]. 3One notices that the error bound for the midpoint rule is one half that of the trapezoidal rule; compare (2) with (3). For a pretty geometrical explanation of why one can expect the midpoint rule t...

Numerical approximations to the Fourier transformed solution of partial differential equations are obtained via Monte Carlo simulation of certain random multiplicative cascades. Two particular equations are considered: linear diffusion equation and viscous Burgers equation. The algorithms proposed exploit the structure of the branching random walks in which the multiplicative cascades are defin...

Seismic interferometry is a field of growing interest in exploration seismology. In this paper we provide the theoretical basis for performing interferometry by deconvolution. We argue that for general models, deconvolution interferometry gives only the causal scattering response between any two receivers, as opposed to cross-correlation which gives both causal and acausal scattering responses....

We consider a family of stationary Navier-Stokes ows parameterized by the Reynolds number. When the Reynolds number tends to in nity, what asymptotic behaviors are observed? This is the problem which we would like to address in the present paper. The most renowned phenomenon is the appearance of the boundary layer. This is wellknown. However, what happens in the ow region away from the boundary...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...