Legendre wavelet-based iterative schemes for fourth-order elliptic equations with nonlocal boundary conditions

In the literature of wavelets, there is limited report of work done to solve nonlinear differential equations with nonlocal boundary conditions. This work is a new attempt to solve a fourth-order elliptic equation with the use of nonlocal boundary conditions by coupling quasilinearization with Legen...

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Bibliographic Details
Published in:Engineering with computers 2020-10, Vol.36 (4), p.1371-1378
Main Authors: Kumar, K. Harish, Vijesh, V. Antony
Format: Article
Language:English
Subjects:
Boundary conditions
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Elliptic functions
Iterative methods
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Nonlinear differential equations
Nonlinear equations
Numerical methods
Original Article
Systems Theory
Wavelet analysis
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Summary:In the literature of wavelets, there is limited report of work done to solve nonlinear differential equations with nonlocal boundary conditions. This work is a new attempt to solve a fourth-order elliptic equation with the use of nonlocal boundary conditions by coupling quasilinearization with Legendre wavelet. Since the previously available approach failed to produce reliable accuracy for certain class of problems, this iterative scheme has been suitably modified to deal with a broader class to obtain an accuracy that is reliable. To show the efficiency of the proposed numerical method, a comparison was performed with some existing methods available in the literature.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-019-00766-5