in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

a numerical method for solving variational problems is presented in this paper. the method is based upon hybrid of hartley functions approximations. the properties of hybrid functions which are the combinations of block-pulse functions and hartley functions are first presented. the operational matrix of integration is then utilized to reduce the variational problems to the solution of algebraic...

A real, square matrix Q is J-orthogonal if Q JQ = J , where the signature matrix J = diag(±1). J-orthogonal matrices arise in the analysis and numerical solution of various matrix problems involving indefinite inner products, including, in particular, the downdating of Cholesky factorizations. We present techniques and tools useful in the analysis, application and construction of these matrices...

Szeg˝ o's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [−1, 1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials Λ, and leads to a new orthogonality structure in the module Λ × Λ. This structure can be interpreted in terms of a 2 × 2 matrix measure on [−1, 1], a...