Error estimation in the integration of ordinary differential equations

Abstract

Linear initial value problems, particularly involving first order differential equations, can be transformed into systems of higher order and treated as boundary value problems. Finite difference analogues considered for obtaining approximate solutions of these boundary value problems are proved to be fourth order convergent processes, by deriving considerable sharper bounds for the discretization error. Numerical examples are given to demonstrate the usefulness of our error bounds.

Keywords:

• Band Matrix
• Monotone Matrix
• Irreducible Matrix
• Difference Equation
• Finite Difference Equation
• Two-Point Boundary Value Problem
• Discretization Error
• Error Bound

Computing Review Categories:

• 5.17