An operational Haar wavelet collocation method for solving singularly perturbed boundary-value problems

SeMA Journal ◽  
2016 ◽  
Vol 74 (4) ◽  
pp. 457-474 ◽  
Author(s):  
Firdous A. Shah ◽  
R. Abass
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Haar Wavelet ◽  
Singularly Perturbed ◽  
Wavelet Collocation Method

An Efficient Wavelet-Based Collocation Method for Handling Singularly Perturbed Boundary-Value Problems in Fluid Mechanics

2017 ◽  
Vol 18 (6) ◽  
pp. 485-494
Author(s):  
Firdous A. Shah ◽  
Rustam Abass
Keyword(s):  
Fluid Mechanics ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Singularly Perturbed ◽  
Test Problems ◽  
Algebraic Equations ◽  
Specific Test

AbstractIn this article, we develop an accurate and efficient wavelet-based collocation method for solving both linear and nonlinear singularly perturbed boundary-value problems that arise in fluid mechanics. The properties of the Haar wavelet expansions together with operational matrix of integration are used to convert the underlying problems into systems of algebraic equations which can be efficiently solved by suitable solvers. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

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