A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

3 Connection matrices 9 3.1 The connection matrix of a graph parameter . . . . . . . . . . . . . . . . . . . . 9 3.2 The rank of connection matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Connection matrices of homomorphisms . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 The exact rank of connection matrices for homomorphisms . . . . . . . . . . . . 13 3.5 Extensions...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Hoffman, Wolfe, and Ho...

in this paper operational matrix of bernstein polynomials (bps) is used to solve bratu equation. this nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. by using operational matrix of fractional integration...

*Correspondence: [email protected] 2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia 3Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt Full list of author information is available at the end of the article Abstract In this article, an accurate and efficient numerical method is presented for solving the space-...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...