Let M (f) denote the midpoint rule and T (f) the trapezoidal rule for estimating ∫ b a f(x) dx. Then Simpson’s rule = M (f) + (1 − )T (f), where = 3 . We generalize Simpson’s rule to multiple integrals as follows. Let Dn be some polygonal region in R; let P0; : : : ; Pm denote the vertices of Dn, and let Pm+1 equal the center of mass of Dn. De4ne the linear functionals M (f) =Vol(Dn)f(Pn+1), wh...

In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, theoretically prove that has convergence rate. To demonstrate effectiveness rate, three experiments are given.

This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develope and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one over the entire real line and then using the trapezoidal rule in order to approximate the transformed integral. This method follows on from the work of Oou...

A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is test...

The purpose of this short communication is to demonstrate the importance of numerical analysis and wavelength increment selection when characterizing fluorescent dissolved organic matter (FDOM) using fluorescence excitation-emission matrix (EEM) regional integration. A variety of water samples, representing a landscape gradient and different types of FDOM, were analyzed for their percentage dis...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

If Visser’s rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of Visser’s rules are admissible is not known. Here we study the situation for specific intermediate logics. We provide natural examples of logics for which Visser’s rule are derivable, admissible b...

A new block method of order two for the numerical solution of initial value problems is derived. This method is similar to the block Trapezoidal rule [12] , where the low power of the block size appear in the principal local truncation error. Direct comparison with result relating to the block Trapezoidal rule results obtained in [1] is made.