Quasi-collocation based on CCC-Schoenberg operators and collocation\n methods

2021/03/12 by Tina Bosner, Bosner, Tina
Engineering · Mathematics · #41A15 #41A25 #41A35 #41A50 #65D07 #65L10 #65L11 #Advanced Numerical Analysis Techniques #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2103.07299

openalex publication_date 2021/03/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We propose a collocation and quasi-collocation method for solving second\norder boundary value problems L₂ y=f, in which the differential operator\nL₂ can be represented in the product formulation, aiming mostly on singular\nand singularly perturbed boundary value problems. Seeking an approximating\nCanonical Complete Chebyshev spline s by a collocation method leads to demand\nthat L₂s interpolates the function f. On the other hand, in\nquasi-collocation method we require that L₂ s is equal to an approximation\nof f by the Schoenberg operator. We offer the calculation of both methods\nbased on the Green's function, and give their error bounds.\n

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