the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlmear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resol...

A new error criterion for the design of FIR filters is proposed. Filters with relatively many free filter coefficients are designed using the Chebyshev, the WLS, and a new partitioned minimax error criterion and the performance of the filters is compared. A general and fast technique for the WLS design is also presented.

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral ...

In this paper we discuss a method to design 2 dimensional (2D) FIR filters with the help of Chebyshev polynomials. The polynomial is first converted into a 2D function and later a mapping function is used to design the filters. By the proposed technique one can design filters with various types of passband.

The Chebyshev or L∞ estimator minimizes the maximum absolute residual and is useful in situations where the error distribution has bounded support. In this paper, we derive the asymptotic distribution of this estimator in cases where the error distribution has bounded and unbounded support. We also consider the asymptotics of set-membership estimators such as the Chebyshev centre and maximum in...

The present study involves a novel computational technique, regarding simultaneous use of the pseudo particle method, Poisson integral method and a special-purpose computer originally designed for molecular dynamics simulations (MDGRAPE-3). In the present calculations, the dynamics of two colliding vortex rings have been studied using the vortex method. The present acceleration technique allows...

In this paper Chebyshev wavelet and their properties are employed for deriving Chebyshev wavelet operational matrix of fractional derivatives and a general procedure for forming this matrix is introduced. Then Chebyshev wavelet expansion along with this operational matrix are used for numerical solution of Bagley-Torvik boundary value problems. The error analysis and convergence properties of t...

A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...