In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

Abstract Suppose a large and dense point cloud of an object with complex geometry is available that can be approximated by smooth univariate function. In general, for such clouds the “best” approximation using method least squares usually hard or sometimes even impossible to compute. most cases, however, “near-best” just as good “best”, but much easier faster calculate. Therefore, fast approach...

This article is devoted to the problem of operator interpolation and functional differentiation. Some information about variational derivatives explicit formulas for exact solutions simplest equations containing first required are given. For functionals defined on sets functions square matrices, various interpolating polynomials Hermitе type with nodes second multiplicity, which contain interpo...

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...

In order to solve Prandtl-type equations we propose a collocation-quadrature method based on de la Vallée Poussin (briefly VP) filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in couple of Hölder-Zygmund spaces locally continuous functions. With respect classical methods Lagrange the same collocation nodes, succeed reproducing optimal rates L2 case cut off...

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 ...