On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative

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McKee, S. and Cuminato, José A. and Mohanty, R. K. (2016) On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative. Neural, Parallel and Scientific Computations, 24. pp. 269-276. ISSN 1061-5369 (http://www.dynamicpublishers.com/Neural/neuralv24....)

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Abstract

This note is concerned with the convergence of a finite difference scheme to the solution of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first derivative. By defining stability as the linear growth of the elements of the inverse of a certain matrix and combining this with consistency, convergence is demonstrated. This stability concept is then interpreted in terms of a root condition.

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