Applications of positive definite matrices in the numericalmethods for ODEs

In designing general linear methods for the numerical soluition of ODEs, a conceptknown as algebraic stability is defined based on a non-linear test problem. By thisconcet, the behavior of the methods applying to the non-linear problems is analyzed.In this paper, we discuss the role of positive definite matrices in defining the algebraicstability and its properties

Keywords:

General linear methods , algebraic stability , symmetric , non-negative definitematrix , positive definite matrix , Second derivative methods