A Comparative Analysis Of Polynomial And Non-Polynomial Spline Approximations In Solving Nonlinear Boundary Value Problems
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Abstract
This paper is a comparative study of the use of spline approximation (polynomial and non-polynomial) in solution of nonlinear two-point boundary value problems (TPBVPs). The study points out the drawbacks of classic cubic polynomial splines in dealing with nonlinearities, stiffness, and oscillativeness, and points out the greater flexibility and accuracy of non-polynomial splines, namely exponential and trigonometric formulations. Analytical analysis and numerical examples show that the exponential spline has superior results in nonlinear and stiff and trigonometric spline has superior results in oscillatory systems. The results validate the fact that non-polynomial splines have better convergence rates, lower error, and better computational stability over polynomial ones.
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