ABOUT THE ORDER OF STABILITY OF THE CONTINUOUS BLOCK BACKWARD DIFFERENCE FORMULA METHODS

Abstract

This article aims to present two important and nice properties for the stability of the continuous block backward difference formula used to solve the initial value problems for ordinary differential equations. These results are extensions (to the step ) of the observations stated for the simple cases of the step  which was given by the author (Dinh Van Tiep, Pham Thi Thu Hang, 2020). These extensions are the useful junctions which enable the proof for the results in that paper to be correct for the general case of the step  Besides, these extensions also provide very nice properties for a class of symmetric polynomials established as a byproduct of the continuous block backward difference formula. These properties are not obvious and not easy to prove. The basis used to prove the results in this article is from the foundation of linear algebra. This basis is even simple, but it gives very nice proof.