Asymptotic stability of numerical methods for linear delay parabolic differential equations

作者：Tian Hongjiong^*

来源：Computers & Mathematics with Applications, 2008, 56(7): 1758-1765.

DOI：10.1016/j.camwa.2008.05.001

• delay parabolic differential equation
• asymptotic stability
• finite difference scheme
• delay-independent
• step-by-step method

This paper is concerned with the asymptotic stability property of some numerical processes by discretization of parabolic differential equations with a constant delay. These numerical processes include forward and backward Euler difference schemes and Crank-Nicolson difference scheme which are obtained by applying step-by-step methods to the resulting systems of delay differential equations. Sufficient and necessary conditions for these difference schemes to be delay-independently asymptotically stable are established. It reveals that an additional restriction on time and spatial stepsizes of the forward Euler difference scheme is required to preserve the delay-independent asymptotic stability due to the existence of the delay term. Numerical experiments have been implemented to confirm the asymptotic stability of these numerical methods.

• 出版日期2008-10
• 单位上海师范大学; 上海大学