The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, i.e., it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with less degrees of freedom as compared to low-order finite element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique...

Abstract This work introduces a new integral transform for functions of exponential order called “NE transform”. We prove some properties NE -transform. Also, applications the NE- to find solution ordinary linear equation are given. The relationships with well-known transforms characterized by identities. study this transform. Then we compare it few exiting in Laplace family such as Laplace, Su...

We propose an efficient computation method for an infinite integral ∞ 0 xdx/(1 + x 6 sin 2 x), which has an unbounded integrand with highly oscillated singularity. Computing the value of this integral has been a problem since 1984. We herein demonstrate that the method using the Hilbert transform to change this type of singular function into a smooth function and compute the value of the integr...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this in...

Attract-Integral ~uations are derived for the ~p~~nta~~on of in-plane as well as transverse displacements of shallow shells undergoing small, quasi-static or dynamic deformations. A combined boundary/interior element method for static stress, free-vibration, and transient response analyses of shallow shells, based on these integral equations, is derived. Numerical results are presented to demon...

In this paper, we study the approximate solution of two-dimensional nonlinear Volterra integral equations by two-dimensional differential transform method. New theorems for the transformation of integrals are introduced and proved. We will give an applicable relation between the two-dimensional nonlinear Volterra integral equations and two-dimensional differential transformation, in order to so...