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.
|Number of pages||8|
|Journal||Neural, Parallel and Scientific Computations|
|Publication status||Published - 31 Aug 2016|
- finite difference
- numerical methods for ODE's
- multistep methods
McKee, S., Cuminato, J. A., & 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, 269-276. http://www.dynamicpublishers.com/Neural/NPSC2016/npsc-278.pdf