This paper analyzes the numerical stability of a class of two-step spline collocation methods for initial value problems for fractional differential equations. The stability region is characterized in terms of the eigenvalues of a power series, which depends on the method parameters. We provide the stability regions for several choices of the method parameters. Numerical experiments prove the effectiveness of the stability results both in a constant stepsize framework and in the case of graded meshes.
Stability of two-step spline collocation methods for initial value problems for fractional differential equations
Cardone A.
;Conte D.;Paternoster B.
2022-01-01
Abstract
This paper analyzes the numerical stability of a class of two-step spline collocation methods for initial value problems for fractional differential equations. The stability region is characterized in terms of the eigenvalues of a power series, which depends on the method parameters. We provide the stability regions for several choices of the method parameters. Numerical experiments prove the effectiveness of the stability results both in a constant stepsize framework and in the case of graded meshes.File in questo prodotto:
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