Analysis of a fourth-order compact $ \theta $-method for delay parabolic equations

Abstract

<abstract><p>The upper bounds for the powers of the iteration matrix derived via a numerical method are intimately related to the stability analysis of numerical processes. In this paper, we establish upper bounds for the norm of the <italic>n</italic>th power of the iteration matrix derived via a fourth-order compact $ \theta $-method to obtain the numerical solutions of delay parabolic equations, and thus present conclusions about the stability properties. We prove that, under certain conditions, the numerical process behaves in a stable manner within its stability region. Finally, we illustrate the theoretical results through the use of several numerical experiments.</p></abstract>