Abstract
In this chapter we consider nonlinear monotone ODEs with Dirichlet boundary conditions. Using a non-equidistant grid we construct an EDS on a three-point stencil and prove the existence and uniqueness of its solution. Moreover, on the basis of the EDS we develop an algorithm for the construction of a three-point TDS of rank \(\bar{m}\,=\,2[(m\,+\,1)/2],{\rm{where}\,{m}}\,\varepsilon\,\mathbb{N}\) is a given natural number and [·] denotes the entire part of the argument in brackets. We prove the existence and uniqueness of the solution of the TDS and determine the order of accuracy. Numerical examples are given which confirm the theoretical results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Basel AG
About this chapter
Cite this chapter
Gavrilyuk, I.P., Hermann, M., Makarov, V.L., Kutniv, M.V. (2011). Three-point difference schemes for monotone second-order ODEs. In: Exact and Truncated Difference Schemes for Boundary Value ODEs. International Series of Numerical Mathematics, vol 159. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0107-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0107-2_3
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0106-5
Online ISBN: 978-3-0348-0107-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)