The stability of multi-step formulae for solving differential equations

Abstract

By the numerical treatment of differential equations, the question of stability is still important. It is advantageous to state alternative methods for investigating the stability of multi-step formulae. Among these methods are: determination of the characteristic roots, graphical method, Hermitian form obtained from the characteristic equation or from the multi-step formula, application of Newton's theorem and using Sturm's theorem. The stability of an illustrative formula is discussed by using each of these methods.

Keywords:

• Stability
• Multi-Step Formula
• Characteristic Roots
• Hermitian Form
• Sturm's Theorem

C.R. Categories:

• 5.17