The paper provides a comparison between two relevant classes of numerical discretizations for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian-dependent Runge–Kutta methods and fully implicit Runge–Kutta methods based on Gauss–Legendre nodes, both A-stable. We show that Jacobian-dependent discretizations are more efficient than Jacobian-free fully implicit methods, as visible in the numerical evidence.

Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems

Conte Dajana;Pagano Giovanni;Paternoster Beatrice
2020-01-01

Abstract

The paper provides a comparison between two relevant classes of numerical discretizations for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian-dependent Runge–Kutta methods and fully implicit Runge–Kutta methods based on Gauss–Legendre nodes, both A-stable. We show that Jacobian-dependent discretizations are more efficient than Jacobian-free fully implicit methods, as visible in the numerical evidence.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4750283
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