this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

‎In this paper‎, ‎we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays‎. ‎Constant or pantograph delays may appear in state-control or both‎. ‎We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then‎, ‎these are utilized to reduce the solution of optimal control with constant...

This article proposes a direct method for solving three types of integral equations with time delay. By using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Numerical examples shows that the proposed scheme have a suitable degree of accuracy.  

this study presents a comparative survey of direct methods for solving variational problems. thisproblems can be used to solve various differential equations in physics and chemistry like rateequation for a chemical reaction. there are procedures that any type of a differential equation isconvertible to a variational problem. therefore finding the solution of a differential equation isequivalen...

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...