A parameter uniform difference scheme for parabolic partial differential equation with a retarded argument

作者：Kaushik Aditya^*; Sharma K K; Sharma Manju

来源：Applied Mathematical Modelling, 2010, 34(12): 4232-4242.

DOI：10.1016/j.apm.2010.04.020

• Convection diffusion
• Delay differential equations
• Dynamical systems
• Numerical modelling
• Parameter estimation
• Decomposition

The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative term is affected by the small parameter. This is precisely the case when the magnitude of the convective term becomes much larger compare to that of diffusion term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other non-linear model equations too.

• 出版日期2010-12