A NEW QUARTIC HYBRID B-SPLINE COLLOCATION FRAMEWORK FOR THIRD ORDER SINGULARLY PERTURBED SINGULAR BOUNDARY VALUE PROBLEMS ARISING IN ENGINEERING APPLICATIONS
DOI:
https://doi.org/10.71146/kjmr664Keywords:
Singular BVPs, Singularly Perturbed BVPs, Hybrid B-Spline, Collocation MethodAbstract
In this study, a numerical computational framework is presented to solve singularly perturbed boundary value problem of the order of 3 using Hybrid Quartic B-spline collocation technique. These problems have a small perturbation parameter and a geometric singularity and narrow boundary layers form which contain a variation of the solution. To overcome these difficulties, we use the quartic B-spline basis functions that map the third order differential equation into a set of linear, algebraic equations that are easily solved. Quartic splines have continuity and provide a smooth approximation to higher order derivatives. Numerical experiments are performed for the verification of accuracy and stability of the method. Comparisons with literature show the present quartic B-spline method has better convergence, and it can effectively solve the multi scale problem.
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Copyright (c) 2025 Ayesha Tanveer, Muhammad Amin, Rabiya Sarwar, Muhammad Mubashar Shahzad (Author)
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