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- Title
On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator.
- Authors
Pitolli, Francesca
- Abstract
Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate.
- Subjects
NUMERICAL solutions to boundary value problems; BOUNDARY value problems; COLLOCATION methods; LAPLACIAN operator; SPLINES; POSITIVE operators; MECHANICAL engineering
- Publication
Axioms (2075-1680), 2020, Vol 9, Issue 2, p61
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms9020061