Numerical Methods with MS Excel

In this note we show how MS Excel can be used to to perform numerical Integration, specifically Trapezoidal Rule and Simson’s rule. Futhermore, we illustrate how to generate Lagranges Interpolation polynomial

Curve Graphing in MS Excel and Applications

Curve sketching is one of the best ways to visualize and investigate the behavior of functions and equations. Graphs convey a lot more information about functions than algebraic expressions would. In this note we shall show how to use MS Excel to graph different types of functions and equations. Applications to zooming, root finding, parametric studies and online curve graphing will be given

A higher-order method for nonlinear singular two-point boundary value problems

We present a finite difference method for a general class of nonlinear singular two-point boundary value problems. The order of convergence of the method for such a general class of problems is higher than the previous reported methods. The method yields a fourth-order convergence for the special case p(x)=w(x)=xα, α≥1

A periodic boundary value problem for nonlinear singular differential systems with ‘maxima’

décembre 20052005/12 (N254)-2005/12.Appartient à l’ensemble documentaire : UnivJeun

An efficient multi-time step FEM–SFEM iterative coupling procedure for elastic–acoustic interaction problems

An iterative coupling methodology between the Finite Element Method (FEM) and the Spectral Finite Element Method (SFEM) for the modeling of coupled elastic-acoustic problems in the time domain is presented here. Since the iterative coupling procedure allows the use of a nonconforming mesh at the interface between the subdomains, the difference in the element sizes concerning the FEM and SFEM is handled in a straightforward and efficient manner, thereby retaining all the advantages of the SFEM. By means of the HHT time integration method, controllable numerical damping can be introduced in one of the subdomains, increasing the robustness of the method and improving the accuracy of the results; besides, independent time-step sizes can be considered within each subdomain, resulting in a more efficient algorithm. In this work, a modification in the subcycling procedure is proposed, ensuring not only an efficient and accurate methodology but also avoiding the computation of a relaxation parameter. Numerical simulations are presented in order to illustrate the accuracy and potential of the proposed methodology.CAPES, UFJF, UFSJ, FAPEMIG and CNP

Weak formulation of singular differential expressions in spaces of functions with minimal derivatives

A weak formulation for singular symmetric differential expressions is presented in spaces of functions which possess minimal differentiability requirements. These spaces are used to characterize the domains of the various operators associated with such expressions. In particular, domains of self-adjoint differential operators are characterized

Curve Graphing in MS Excel and Applications

Curve sketching is one of the best ways to visualize and investigate the behavior of functions and equations. Graphs convey a lot more information about functions than algebraic expressions would. In this note we shall show how to use MS Excel to graph different types of functions and equations. Applications to zooming, root finding, parametric studies and online curve graphing will be given