A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed. Keywords: Two-step collocation methods • Order conditions • Absolute stability • A-stability • Local error estimation
Two step almost collocations methods for Ordinary Differential Equations
D'AMBROSIO, RAFFAELE;PATERNOSTER, Beatrice
2010
Abstract
A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed. Keywords: Two-step collocation methods • Order conditions • Absolute stability • A-stability • Local error estimationFile in questo prodotto:
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