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About 10,000 papers for “Variational method”

Variational Iteration Method Variational Approach Method

S. Alinia, M. Ghadimi, H. D. Kaliji et al. · 2013

Abstract: In this study, a nonlinear oscillation system is investigated with two analytical methods called Variational Iteration Method (VIM) and Variational Approach Method (VAM). The governing equation of system is obtained by using Lagrange method and then nonlinear governing equation is analyzed by VIM and VAM. The results reveal that the VIM and VAM can achieve suitable results in predicting the solution of such th problems. After verification with Runge-Kutta 4 order method, we consider the effects of some physical applicable in this problem.

Cited by 0

Variational Method

Chi-Wah Kok, Wing-Shan Tam · 2024

One of the models developed for the regularization function is the total variation. The total variation model relies on the flow of gradient descent of the image smoothness. This chapter has reformulated the Wiener filter image denoising problem with the help of a regularization function to a total variation optimization problem. It discusses a number of total variation regularization functions, and in particular, it shows how to apply the Rudin-Osher-Fatemi (ROF) model to construct the regularization function for image denoising. The finite difference is applied to implement the ROF total variation image denoising algorithm in MATLAB. The ROF total variation denoising method has shown to be a mathematically tractable method that can produce nice denoise results. However, it has its disadvantages, which include over-smoothing, and in some cases, with the multiplier poorly chosen, a cartoon-like appearance of the denoised image will result.

Cited by 0

Variational Method

Владимир И. Минкин · IUPAC Standards Online · 2016

The glossary contains definitions and explanatory notes for more than 450 terms used in the context of multidisciplinary research and publications related to applications of modern theoretical concepts, computational and graph-theoretical methods to investigation into structure, reactivity, spectroscopic and other physical and physicochemical properties of organic, organometallic and metal coordination compounds. The aim of the glossary is to provide guidance on terminology used in theoretical organic chemistry and to contribute to the elimination of inconsistencies and ambiguities in the meanings of terms in the area.

Cited by 0Open access

Variational Iteration Method

Snehashish Chakraverty, Nisha Rani Mahato, Perumandla Karunakar et al. · 2019

The variational iteration method (VIM) is one of the well-known semi-analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well. By this method one can find the convergent successive approximations of the exact solution of the differential equations if such a solution exists. Wazwaz used the VIM for solving the linear and nonlinear Volterra integral and integro-differential equations and explained clearly how to use this method for solving homogenous and inhomogeneous partial differential equations. This chapter solves few test problems using the present method to make the readers familiar with the method. As such, two linear nonhomogeneous partial differential equations are handled in two examples, and a nonlinear partial differential equation has been solved in other example.

Cited by 2

Variational Iterative Method

Snehashish Chakraverty, Rajarama Mohan Jena, Subrat Kumar Jena · 2022

Variational iterative method (VIM) is again a semi-analytical technique like homotopy perturbation method (HPM) and Adomian decomposition method (ADM) for solving both linear and nonlinear ordinary/partial/fractional differential equations. This technique is based on the application of restricted variations and correction functional. VIM does not require small parameters in the differential equation and generates a solution as a sequence of iterations. It does not need the nonlinearities to be differentiable with respect to the dependent variable and its derivatives. This chapter first discusses the fundamental concept of VIM. Further, this method is used to deal with two problems: a linear one-dimensional fractional heat-like equation and a nonlinear fractional advection equation. The test problems used in this chapter indicate that VIM is an effective way to solve linear/nonlinear fractional differential equations. The series generally converges with an increase in terms, but the compact solution form may not always be expected.

Cited by 1