A Collocation Method for the Gurtin--MacCamy Equation with Finite Life-Span

Authors:
Mi-Young Kim;Yonghoon Kwon
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2001

Citing 0
Cited 3

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Abstract

A collocation method along the characteristics for a stiff problem arising from population dynamics is proposed and analyzed. It is a fourth order implicit Runge--Kutta method of two stage to the integration of the ODE along the characteristics, whose collocation points are zeros of the linearly transformed Legendre monic polynomial. Nonnegativity of the numerical solutions is shown. The stability of the method is discussed. It is proven that the scheme is convergent at a fourth order rate in the maximum norm. Several numerical examples are presented.