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

S. McKee, José A. Cuminato, R. K. Mohanty

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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.
Original languageEnglish
Pages (from-to)269-276
Number of pages8
JournalNeural, Parallel and Scientific Computations
Volume24
Publication statusPublished - 31 Aug 2016

Keywords

  • finite difference
  • numerical methods for ODE's
  • multistep methods

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