In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

An extension of the GCED matrices from domain natural integers to unique factorization is given. The structure these type defined on both arbitrary sets and GCED-closed are presented. Moreover, we present exact expressions for determinant inverse such matrices. domains Gaussian polynomials over finite fields used illustrate work.

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear m...

In this work, a new approach of the Kekre transform in the integral form is introduced. A theory of operation matrix is developed by numerical computation and by partitioning of the matrices in four submatrices which is proved as the same. An operational matrices of integration based on Kekre transform are applied to the dynamic systems with distributed parameters to analyse their applications....

The so-called modified transform (T) graphs are described in the paper, which are a graph analogy to wellknown voltage and current incidence matrices. The procedure is shown how to pass from T-graphs to the classical Mason-Coates (MC) flow graph. The explanation is illustrated with examples of circuits containing operational amplifiers and current conveyors. Key-Words: Signal flow graph, flow g...