摘要
This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.
This paper investigates the stability and convergence of some known difference schemes for the numerical solution to heat conduction equation with derivative boundary conditions by the fictitious domain method.The discrete vari- ables at the false mesh points are firstly eliminated from the difference schemes and the local truncation errors are then analyzed in detail.The stability and convergence of the schemes are proved by energy method.An improvement is proposed to obtain better schemes over the original ones.Several numerical examples and comparisons with other schemes are presented.
