An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is described. The method is based on multi-dimensional second generation wavelets, and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems [Int. J. Comp. Fluid Dyn. 17 (2003) 151]. Wavelet decomposition is used fo...

Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools that provide good mathematical model for scientific phenomena, whic...

In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.

Abstract In this paper, a two-dimensional steady flow of viscous fluid due to stretching sheet in the presence magnetic field is considered. We proposed two new numerical schemes based on Haar wavelet coupled with collocation approach and quasi-linearization process for solving Falkner-Skan equation representing governing problem. The important derived quantities velocity wall shear stress vari...

In this paper a novel invisible robust watermarking scheme for embedding and extracting a digital watermark in an image is presented. The novelty lies in determining perceptually important coefficients of transform in the host image using simple Haar Wavelet Transform (HWT) and Genetic Algorithm(GA)-Particle Swarm Optimization(PSO) based hybrid optimization. Invisible watermark is embedded such...

This paper presents a hybrid scheme based on Dinkelbach approach and wavelet collocation method to extract approximate solutions of fractional optimal control problems (FOCP)’s. First Dinkelbach approach is considered to linearize the problem, then it is tried by combination of collocation wavelet approach and a numerical scheme of solving nonlinear equations, an iterative approach be proposed ...

On Time Fractional Modifed Camassa-Holm and Degasperis-Procesi Equations by Using the Haar Wavelet Iteration Method

A short review of wavelet-based adaptive methods for modeling and simulation incompressible turbulent flows is presented. Wavelet-based computational approaches different fidelities are recast into an integrated hierarchical eddy-capturing turbulence framework. The wavelet threshold filtering procedure the associated wavelet-filtered Navier–Stokes equations briefly discussed, along with colloca...