Finite and Infinite Dimensional Reproducing Kernel Hilbert Space Approach for Bagley–Torvik Equation

In this paper, two different numerical approaches are presented in finite dimensional and infinite dimensional reproducing kernel Hilbert spaces for the fractional order Bagley–Torvik equation with boundary conditions. The reproducing kernel functions are obtained in finite dimensional Hilbert space...

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Bibliographic Details
Published in:International journal of applied and computational mathematics Vol. 11; no. 1; p. 18
Main Authors: Ata, Ayşe, Sakar, Mehmet Giyas, Saldır, Onur, Şenol, Mehmet
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.02.2025
Springer Nature B.V
Subjects:
Applications of Mathematics
Approximation
Boundary conditions
Boundary value problems
Computational Science and Engineering
Engineering
Graphical representations
Hilbert space
Kernel functions
Mathematical analysis
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Methods
Nuclear Energy
Operations Research/Decision Theory
Ordinary differential equations
Original Paper
Partial differential equations
Physics
Polynomials
Theoretical
Numerical approximation
Reproducing kernel method
Bagley–Torvik equation
Boundary value problem
Shifted Legendre polynomials
ISSN:2349-5103, 2199-5796
Online Access:Get full text
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Summary:In this paper, two different numerical approaches are presented in finite dimensional and infinite dimensional reproducing kernel Hilbert spaces for the fractional order Bagley–Torvik equation with boundary conditions. The reproducing kernel functions are obtained in finite dimensional Hilbert space Π ρ n [ 0 , A ] using Legendre polynomials, while they are obtained by a known classical method in infinite dimensional Sobolev-Hilbert space W 2 3 [ 0 , A ] . A comprehensive theoretical analysis is given for both approaches, which have different forms of reproducing kernel methods. Numerical results are calculated over wide intervals with both proposed approaches. In order to compare the efficiency of these proposed methods, the numerical results obtained for the considered six examples are presented through tabulated data and graphical representations.
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ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-024-01828-z