An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations

Wind energy is one of the speedy processing technologies in the energy generation industry and the most economical methods of electrical power generation. For the reliability of system, it is wanted to improve highly appropriate wind speed forecasting methods. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. This technique has proven useful in a nonstationary time series forecasting. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Lucas polynomials, as well as a comparison between an artificial neural network (ANN) and wavelet-artificial neural network (WNN). We used the proposed wavelet, Mexican hat, Morlet, Gaussian, Haar, Daubechies, and Coiflet to transform the wind speed data using the continuous wavelet transform (CWT). MATLAB software was used to implement the CWT and ANN. The proposed models were applied in the meteorological field to forecast the daily wind speed data that were collected from the meteorological directorate of Sulaymaniyah which is a city located in the Kurdistan region of Iraq for the period (Jan. 2011–Dec. 2020). Five different performance criteria during calibration and validation, the root mean square error ( R M S E ), mean square error ( M S E ), mean absolute percentage error M A P E , mean absolute error M A E , and coefficient of determination ( R 2 ), were evaluated. When studying, analyzing, and comparing these models, the results of the study concluded that the proposed wavelet-ANN is the best result ( M S E = 0.00072 , R M S E = 0.02683 , M A P E = 2.32400 , and R 2 = 0.99983 .

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“…It is defned as the sum of the two terms immediately preceding it. Te recurrence relation gives Lucas polynomials [38].…”

Section: Methodsmentioning

confidence: 99%

Forecasting Wind Speed Using the Proposed Wavelet Neural Network

Mohammed

Ahmed

2023

Discrete Dynamics in Nature and Society

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“…e same author studied the solution of logarithmic singular boundary integral equations which arise from the Laplace equation using meshless Galerkin scheme based on radial basis function [19,20]. Similarly, other numerical techniques are used for approximate solution of different class of PDEs in [21][22][23][24] and the reference there in.…”

Section: Introductionmentioning

confidence: 99%

A Mesh-Free Collocation Method Based on RBFs for the Numerical Solution of Hunter–Saxton and Gardner Equations

Ullah

Ali

Shaheen

et al. 2022

Mathematical Problems in Engineering

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In this paper, the radial basis function (RBF) collocation method is applied to solve nonlinear partial differential equations (PDEs). First, the given equation is reduced to time-discrete form using Ө-weighted scheme. Then, with the help of RBFs, the given PDEs are transformed into a system of algebraic equations that is easy to solve. The proposed technique is verified by solving Hunter–Saxton and Gardner equations. For the solution of these problems, three types of RBFs, including multiquadric (MQ), inverse multiquadric (IMQ), and Gaussian (GA) have been used. The obtained solution is validated with the help of absolute error, L2, and L∞ error norms. The involved shape parameter is selected by the automatic algorithm that lies in the stable region of the method. The stability of the scheme is discussed by the spectral matrix method and validated computationally.

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“…In addition, coupled systems of fractional differential equations have attracted particular concern from scholars considering their appearance in the mathematical modeling of physical phenomena like chaos synchronization [5], anomalous diffusion [6], disease models [7], and so on. The existence theory to fractional differential equations with integral boundary conditions has widespread applications in optimization theory, many researchers have studied [8][9][10][11][12][13], and the existence of solutions is the basis of studying the stability and numerical solutions of differential equations [14]. For the existence of solutions of fractional differential equations, the authors use diverse methods, such as fixed point theory [15][16][17][18][19], upper and lower solutions method [20], monotone iterative technique and Mawhin's continuation theorem [21], and topological degree theory [22].…”

Section: Introductionmentioning

confidence: 99%