Approximate Solutions for Undamped Nonlinear Oscillations Using He’s Formulation

Approximate Analytical Solutions to Nonlinear Oscillations of Non-natural Systems Using He’s Energy Balance Method

This paper applies He’s Energy balance method (EBM) to study periodic solutions of strongly nonlinear systems such as nonlinear vibrations and oscillations. The method is applied to two nonlinear differential equations. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with exact solutions which lead us showing a good accuracy. The m...

Approximate Solutions of Nonlinear Conservation Laws

This is a summary of ve lectures delivered at the CIME course on "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" held in Cetraro, Italy, on June 1997. Following the introductory lecture I | which provides a general overview of approximate solution to nonlinear conservation laws, the remaining lectures deal with the speciics of four complementing topics: Lecture II. Finite-d...

Error Estimates of Approximate Solutions for Nonlinear Scalar Conservation Laws

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...

Error Estimate for Approximate Solutions Ofa Nonlinear Convection - Diffusion

OPTIMIZATION FORMULATION FOR NONLINEAR STRUCTURAL ANALYSIS

In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was p...