In this paper, we propose a modified method for the circuit analysis using wavelet transform with adaptive resolutions. Recently, many approaches to the circuit analysis using the wavelet transform have been proposed. Previously, we proposed method which can choose adaptive resolution automatically using multiresolution analysis. However, the method cannot be applied when the waveform has the s...

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...

In this paper we present an adaptive multilevel total variational (TV) method for image denoising which utilizes TV partial differential equation (PDE) models and exploits the multiresolution properties of wavelets. The adaptive multilevel TV method provides fast adaptive wavelet-based solvers for the TV model. Our approach employs a wavelet collocation method applied to the TV model using two-...

We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the non...