The use of Walsh-wavelet packets in linear boundary value problems

Glabisz, W.

doi:10.1016/j.compstruc.2003.10.004

Cited by 10 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As noted in [3] and [4], second-order boundary value problems (BVPs) have important uses in the field of mathematical modeling in situations such as the displacement analysis of cantilever beams under concentrated tension, plate perversion theories, and the investigation of ray distortion. Several writers have explored the numerical solution of second-order BVPs, demonstrating the variety of methods in this field [5,6].…”

Section: Introductionmentioning

confidence: 99%

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

Sayed,

Mohamed,

El-Dahab

et al. 2024

Contemp. Math.

View full text Add to dashboard Cite

This article introduces two numerical methods to address boundary value problems associated with secondorder and fractional differential equations. These methods employ two parameters related to shifted Gegenbauer polynomials as their basis functions. The process involves establishing a differentiation operational matrix for the shifted Gegenbauer polynomials. Subsequently, the initial/boundary value problems for ordinary and fractional differential equations are transformed into a system of equations through the Galerkin, collocation, and tau methods. The convergence analysis is ensured by leveraging theorems pertaining to the shifted Gegenbauer polynomials. To validate the accuracy of the approach, numerous numerical examples are presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

Sayed,

Mohamed,

El-Dahab

et al. 2024

Contemp. Math.

View full text Add to dashboard Cite

show abstract

“…Second-order multipoint boundary value problems (BVP) arise in the mathematical modeling of deflection of cantilever beams under concentrated load [21,22], deformation of beams and plate deflection theory [23], obstacle problems [24], Troesch's problem relating to the confinement of a plasma column by radiation pressure [25,26], temperature distribution of the radiation fin of trapezoidal profile [21,27], and a number of other engineering applications. Many authors have used numerical and approximate methods to solve second-order BVPs.…”

Section: Introductionmentioning

confidence: 99%

“…Many authors have used numerical and approximate methods to solve second-order BVPs. The details about the related numerical methods can be found in a large number of papers (see, for instance, [21,23,24,28]). The Walsh wavelets and the semiorthogonal B-spline wavelets are used in [23,29] to construct some numerical algorithms for the solution of second-order BVPs with Dirichlet and Neumann boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The details about the related numerical methods can be found in a large number of papers (see, for instance, [21,23,24,28]). The Walsh wavelets and the semiorthogonal B-spline wavelets are used in [23,29] to construct some numerical algorithms for the solution of second-order BVPs with Dirichlet and Neumann boundary conditions. Na [21] has found the numerical solution of second-, third-, and fourth-order BVPs by converting them into initial value problems and then applying a class of methods like nonlinear shooting, method of reduced physical parameters, method of invariant imbedding, and so forth.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds

Abd-Elhameed

Doha

Youssri

2013

Abstract and Applied Analysis

View full text Add to dashboard Cite

This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorably with the analytical known solutions.

show abstract

Based on Walsh packet parametric identification technique for dynamic systems

Napiórkowska-Ałykow

Glabisz

2005

Proc Appl Math and Mech

View full text Add to dashboard Cite

The article presents an application of wavelet packet analysis in the parametric identification of discrete dynamic systems. The Walsh packet basis and their operational matrixes enables reduction of row derivatives, which are necessary in the procedure of identification of signal derivatives for systems, which are analyzed, and also enable algebraization their mathematical describe, what in combination with wavelet packet analysis with Haar filter properties decided on a great efficiency of parametric identification of linear systems procedure, which is built on wavelet packet analysis. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

show abstract

The use of Walsh-wavelet packets in linear boundary value problems

Cited by 10 publications

References 15 publications

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

Alleviated Shifted Gegenbauer Spectral Method for Ordinary and Fractional Differential Equations

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds

Based on Walsh packet parametric identification technique for dynamic systems

Contact Info

Product

Resources

About