Non-orthogonal spline wavelets are developed for Galerkin BEM. The proposed wavelets have compact supports and closed-form expressions. Besides of it, one can choose arbitrarily the order of vanishing moments of the wavelets independently of order of B-splines. Sparse coefficient matrices are obtained by truncating the small elements a priori. The memory requirement and computational time can b...

The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order (the corresponding eigenvalue order) depend on a doublet of parameters ( , ); we extend results derived for the special case = = 1 and include a proof of “the resolution...

We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the conventionally defined renormalized operator to couple to the source. However, in four dimensions, the effective potential for the conventional renormalized com...

As one of the most widespread renewable energy sources, wind is now an important part power system. Accurate and appropriate speed forecasting has essential impact on utilisation. However, due to stochastic uncertain nature energy, more accurate necessary for its stable safer This paper proposes a Legendre multiwavelet-based neural network model non-linear prediction. It combines excellent prop...

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal sets that aim to minimise the L∞ error interpolating polynomial. The present work combines comprehensive review known approximation theory results, with new numerical experiments, mo...