We consider a class of explicit numerical methods used for solving Ordinary Differential Equations (ODEs). These methods are called peer methods. In this talk we derive the coefficients of following a different path than the classical one, using the approach that was applied on explicit two- and three-stage Runge-Kutta methods, obtaining coefficients that depend on the Jacobian of f. This technique improves the stability and accuracy properties of existing peer methods, making them useful for solving stiff ODEs. We conduct numerical experiments in order to confirm theoretical properties of these new methods.

Jacobian-dependent peer methods for ordinary differential equations

Conte Dajana;Pagano Giovanni
;
Paternoster Beatrice
2021-01-01

Abstract

We consider a class of explicit numerical methods used for solving Ordinary Differential Equations (ODEs). These methods are called peer methods. In this talk we derive the coefficients of following a different path than the classical one, using the approach that was applied on explicit two- and three-stage Runge-Kutta methods, obtaining coefficients that depend on the Jacobian of f. This technique improves the stability and accuracy properties of existing peer methods, making them useful for solving stiff ODEs. We conduct numerical experiments in order to confirm theoretical properties of these new methods.
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4769528
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