in this research three-dimensional free vibration analysis of functionally graded circular plate with various boundary conditions is achieved. a semi-analytical method, which makes use of the state space method and the one-dimensional differential quadrature method, is used to obtain the vibration frequencies and dynamic responses of circular plates. numerical results are given to demonstrate t...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

In this paper we present an adaptive multi-element generalized polynomial chaos (ME-gPC) method, which can achieve hp-convergence in random space. ME-gPC is based on the decomposition of random space and generalized polynomial chaos (gPC). Using proper numerical schemes to maintain the local orthogonality on-the-fly, we perform gPC locally and adaptively. The key idea is to combine the polynomi...

Exact analytical solutions of the equations of motion exist only for simple systems, of the types that are discussed in elementary classical mechanics courses, and therefore numerical integration methods are very important in practice. Here we will discuss some commonly used differential equation solvers and use them to study the dynamics of mechanical systems, including ones that exhibit chaot...

We present details of the 1D PDE solver used in the OpenGamma Platform, showing how it can price European and American options, with and without barrier features. All the results in this paper we generated using MATLAB, and this code is included here www.opengamma.com/downloads/financial-pde-solving-matlab-examples.zip.

We propose a numerical approach for solving systems of nonautonomous ordinary differential equations under suitable assumptions. This approach is based on expansion of the solutions by Volterra series and allows to estimate the accuracy of the approximation. Also we can solve some ordinary differential equations for which the classical numerical methods fail.

In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations...

Portfolio management can be eeectuated through solutions to stochastic optimal control problems. Few problems of that kind can be solved analytically. A numerical method based on a simple Markovian approximation is described and applied to a classical optimal portfolio selection problem. Numerical solutions of varying degree of accuracy are obtained. Solutions are computed to a few important sp...

The stability of imperfect cartel, i.e. a market with both cartel firms (k-firms) and noncartel or fringe firms (j-firms), has a long research history. Selten (1973) was the first to argue that four firms in a market are a few while six are too many. Ten years later, D'Aspremont et al (1983), modelled the behavior of j-firms as price-takers. Donsimoni et al (1986) and Daskin (1989), based on D'...