The continuous wavelet transform is already a well established procedure for analysing data. Its main advantages over the classical Fourier transform are its local and multiresolution nature, which provide the interesting properties of a mathematical microscope. Its theory is well known in the case of the line and plane. However, the representation and analysis of signals in non-Euclidean geome...

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of fin, various methods have been applied to solve the nonlinear thermal models. This paper focuses...

The development and production of high performance equipment necessitate the use of passive cooling technology. In this paper, heat transfer study of convective-radiative straight fin with temperature-dependent thermal conductivity under the influence of magnetic field is carried out using Legendre wavelet collocation method. The numerical solution is used to investigate the effects of magnetic...

In this work, Laplace transform-Legendre-wavelet collocation method is adopted for a semi-numerical analysis of predicting transient nonlinear behaviour radiative-convective fin with temperature-variant internal heat generation. The verification the results hybrid shown good agreements direct numerical and approximate analytical s in previous works. Parametric depicts significance model paramet...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

In our paper we construct a polynomial Schauder basis (pα,β,n)n∈N0 of optimal degree with Jacobi orthogonality. A candidate for such a basis is given by the use of some wavelet theoretical methods, which were already successful in case of Tchebysheff and Legendre orthogonality. To prove that this sequence is in fact a Schauder basis for C[−1, 1] and as the main difficulty of the whole proof we ...

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the mu...