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

03/12/2021

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by   Tina Bosner, et al.

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We propose a collocation and quasi-collocation method for solving second order boundary value problems L_2 y=f, in which the differential operator L_2 can be represented in the product formulation, aiming mostly on singular and singularly perturbed boundary value problems. Seeking an approximating Canonical Complete Chebyshev spline s by a collocation method leads to demand that L_2s interpolates the function f. On the other hand, in quasi-collocation method we require that L_2 s is equal to an approximation of f by the Schoenberg operator. We offer the calculation of both methods based on the Green's function, and give their error bounds.