A simple, novel, efficient and three-component procedure for the synthesis of pyrimido[4,5-d]pyrimidine-2,4-dione derivatives by the reaction of 6-amino-1,3-dimethyluracil, aldehyde and 2-benzylisothiourea hydrochloride promoted by ionic liquid 1-butyl-3-methylimidazolium bromide ([BMIm]Br) under solvent-free conditions is reported. The presented method is benefited from operational simplicity...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

the three components one pot synthesis of 2-amino-4h-benzo-[b] -pyran derivatives were obtained in good to excellent yields within short reaction time by condensing dimedone, aldehydes and malanonitrile or ethylcyanoacetate using a catalytic amount of (diacetoxyiodo)benzene as hypervalent iodine in aqueous ethanol under reflux conditions have been discussed. this aqua mediated knoevenagel-cyclo...

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 article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

A practical and green approach for the one-pot multicomponent synthesis of fused tetrazolo[1,5-a]quinazoline derivatives has been described via the condensation of 5- aminotetrazole, dimedone, and various aldehydes using 1-butyl-3-methylimidazolium tetrachloroaluminate [bmim]Cl/AlCl3, as a catalyst and task-specific ionic liquid medium. The catalyst was showed remarkable advantages in compariso...

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...