In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

(Diacetoxyiodo)benzene has been used as an efficient catalyst for an improved and rapid one-pot synthesis of biscoumarin derivatives in excellent yield under reflux condition using water as a environmentally benign reaction medium. This aqua mediated Knoevenagel condensation of various aromatic and hetero-aromatic aldehydes with 4-hydroxycoumarin using catalytic amount of (diacetoxyiodo)benzene...

In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series to...

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the accuracy of the method, five numerical problems, such as the human head, Oxygen diffusion and Bessel differential equation, were ...

(Diacetoxyiodo)benzene has been used as an efficient catalyst for an improved and rapid one-pot synthesis of biscoumarin derivatives in excellent yield under reflux condition using water as a environmentally benign reaction medium. This aqua mediated Knoevenagel condensation of various aromatic and hetero-aromatic aldehydes with 4-hydroxycoumarin using catalytic amount of (diacetoxyiodo)benzene...