I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method ...

A new method, termed probability perturbation, is developed for solving nonlinear inverse problem under a prior model constraint. The method proposed takes a different route from the traditional Bayesian inverse models that rely on prior and likelihood distribution for stating, then sampling, from a posterior distribution. Instead, the probability perturbation method relies on so-called pre-pos...

We formulate a coupled vibration problem between a structure and an acoustic field by FEM. The problem leads to a non-standard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with ...

ultivariate stochastic optimization plays a major role in the analysis and control of many engineering systems. In almost all real-world optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In this spirit, the “simultaneous perturbation stochastic approximation (SPSA)” met...

and Applied Analysis 3 Accordingly, we can construct a homotopy equation in the form ü ω2u p ( u3 −ω2u ) 0. 2.6 When p 0, we have ü ω2u 0, u 0 A, u′ 0 0, 2.7 which describes the basic solution property of the original nonlinear equation, 2.3 . When p 1, 2.6 becomes the original one. So the solution procedure is to deform from the initial solution, 2.4 , to the real one. Due to one unknown param...

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. Obtaining the physically relevant quantity from the measured one requires, therefore ...