Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets

Rayal, Ashish; Verma, Sag Ram

doi:10.1177/1077546320974792

Cited by 10 publications

(4 citation statements)

References 37 publications

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“…Several researchers have used wavelet-based approximation approaches to solve different classes of differential equations. See these references [15][16][17][18][19][20] for more applications of wavelets.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets

et al. 2023

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This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived by means of fractional Bernstein polynomials. The oscillation equation describes electrical circuits and exhibits a wide range of nonlinear dynamical behaviors. The proposed variable order model is of current interest in a lot of application areas in engineering and applied sciences. The purpose of this study is to analyze the behavior of the fractional force-free and forced oscillation equations under the variable-order fractional operator. The basic idea behind using the approximation technique is that it converts the proposed model into non-linear algebraic equations with the help of collocation nodes for easy computation. Different cases of the proposed model are examined under the selected variable order parameters for the first time in order to show the precision and performance of the mentioned scheme. The dynamic behavior and results are presented via tables and graphs to ensure the validity of the mentioned scheme. Further, the behavior of the obtained solutions for the variable order is also depicted. From the calculated results, it is observed that the mentioned scheme is extremely simple and efficient for examining the behavior of nonlinear random (constant or variable) order fractional models occurring in engineering and science.

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Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets

et al. 2023

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“…In the work that is presented in [7], the direct method of differential transform method was employed for solving certain problems in the calculus of variations. The authors of [8] solved the variational problems of fixed or moving boundary conditions by an approximation method based on the operational matrix of integration for Muntz wavelets. An iterative technique for the approximate solution is applied to the calculus of variation in [9].…”

Section: Introductionmentioning

confidence: 99%

Boubaker Scaling Operational Matrices for Solving Calculus of Variation Problems

Ouda,

Ibraheem,

SHIHAB

2023

Iraqi Journal of Science

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In this paper, a general expression formula for the Boubaker scaling (BS) operational matrix of the derivative is constructed. Then it is used to study a new parameterization direct technique for treating calculus of the variation problems approximately. The calculus of variation problems describe several important phenomena in mathematical science. The first step in our suggested method is to express the unknown variables in terms of Boubaker scaling basis functions with unknown coefficients. Secondly, the operational matrix of the derivative together with some important properties of the BS are utilized to achieve a non-linear programming problem in terms of the unknown coefficients. Finally, the unknown parameters are obtained using the quadratic programming technique. Some numerical examples are included to confirm the accuracy and applicability of the suggested direct parameterization method.

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“…[12] Found the approximate solution for boundary value problems using the wavelet function. [13] Studied moving or fixed boundary Muntz wavelets for solving variation problems. This paper is arranged as follows: in Section 2, Orthogonal Boubaker polynomials and their properties with recurrence relations In Section 3, Boubaker wavelets and their properties In Section 4, the application of Boubaker wavelet polynomials for solving variational problems with some numerical examples has been presented.…”

Section: Introductionmentioning

confidence: 99%

Direct Method for Variational Problems Using Boubaker Wavelets

Ouda

2023

IHJPAS

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The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Different numerical examples were given to demonstrate the applicability and validity of this method using the Matlab program. Also, the results of this technique were compared with the exact solution, and graphs were added to these examples to test the convergence of Wavelet Boubaker polynomials using this method.

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Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets

Cited by 10 publications

References 37 publications

Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets

Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets

Boubaker Scaling Operational Matrices for Solving Calculus of Variation Problems

Direct Method for Variational Problems Using Boubaker Wavelets

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