IJAM, Volume 26, No. 4 (2013)

Abstract. In this paper, long time error estimate for the nerve axon type equations is obtained using a non-traditional method. Traditional methods for analyzing exact error propagation depends on the stability of the numerical method. Whereas, in this paper the analysis of the exact error propagation use attractors which only depends on the stability of the dynamical system. The use of the smoothing indicator yields a posteriori estimates on the numerical error instead of a priori estimates.