Global error estimates for a uniparametric family of stiffly accurate Runge-Kutta collocation methods on singularly perturbed problems |
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Authors: | S González-Pinto D Hernández-Abreu |
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Institution: | 1.Departamento de Análisis Matemático,Universidad de La Laguna,La Laguna,Spain |
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Abstract: | An error analysis for a newly defined uniparametric family of stiffly accurate Runge-Kutta collocation methods when applied
to initial value problems for singularly perturbed differential equations is carried out. The so-called SAFERK methods possess a first internal stage of explicit type and are based on collocation nodes. Sharp convergence results are
obtained for these methods through the analysis of a sequence of higher index Differential Algebraic Equations. A numerical
test with the Van der Pol oscillator reveals that the proposed error estimates are realistic whenever the stepsize h is large enough compared to the stiffness parameter ε. |
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