Solving Reaction-Diffusion and Advection Problems with Richardson Extrapolation

Table 1

Absolute error of the diffusion problem without and with passive/active Richardson extrapolation (with the estimated convergence order in parentheses).

Time step	Absolute error
	Euler		Passive Richardson		Active Richardson
		—		—		—
		(1.000)		(2.019)		(1.991)
		(1.000)		(2.027)		(1.987)
		(1.000)		(2.035)		(1.978)
		(1.000)		(2.043)		(1.971)
		(1.000)		(2.054)		(1.961)
		(1.000)		(2.117)		(1.852)
		(1.000)		(2.109)		(1.413)
		(1.000)		(1.183)		(0.934)
		(1.000)		(0.520)		(0.650)
		(1.000)		(0.252)		(0.308)
		(1.000)		(0.016)		(0.024)
		(1.000)		(−0.004)		(−0.001)
		(0.999)		(0.000)		(0.000)
		(0.997)		(−0.001)		(0.001)
		(0.991)		(0.000)		(0.000)
		(0.975)		(0.002)		(0.000)