A numerical technique is presented for the solution of Falkner-Skan equation. The nonlinear ordinary differential equation is solved using Chebyshev cardinal functions. The method have been derived by first truncating the semi-infinite physical domain of the problem to a finite domain and expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the oper...

An infinite Markov system {f0, f1, . . . } of C2 functions on [a, b] has dense span in C[a, b] if and only if there is an unbounded Bernstein inequality on every subinterval of [a, b]. That is if and only if, for each [α, β] ⊂ [a, b] and γ > 0, we can find g ∈ span{f0, f1, . . . } with ‖g′‖[α,β] > γ‖g‖[a,b]. This is proved under the assumption (f1/f0)′ does not vanish on (a, b). Extension to hi...

A method of constructing a Chebyshev approximation multivariable functions by generalized polynomial with the exact reproduction its values at given points is proposed. It based on sequential construction mean-power approximations, taking into account interpolation condition. The calculated using an iterative scheme least squares variable weight function. An algorithm for calculating parameters...

Spectral methods approximate functions by projection onto a space PN of orthogonal polynomials of degree ≤ N . When the underlying function is periodic trigonometric (Fourier) polynomials are employed while a popular choice for non-periodic functions are the Chebyshev polynomials. Legendre polynomials are another option in the non-periodic case but are not as popular in applications due to the ...

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...