abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

Feasibility of using Cyanex 301, as the auxiliary agent, for supercritical extraction of Cupper and Manganese cations from solid matrix was studied statistically. The amount of extraction is influenced by several parameters, such as amount of ligand, pressure, temperature, SCCO2 flow rate, time of extraction and amount of acid. Recent researches showed that factorial design is an effective tool...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers Basset force’s fractional origin and contains Riemann–Liouville integral rewritten as a Grunwald–Letnikov derivative. As result, general solution proposed found analytically. The belonging to real range values strictly theoretically proven. obtained validated on particular analytical...

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

*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-...

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems FDEs. The main goal method is convert FDE into a system algebraic equations that can be easily solved using matrix methods. In order achieve this, we first generate operational matrices for fractional integration and block-pulse functions (BPF) function approximation. Since obtained sparse, numerical fast...

The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convol...