A Crank-Nicolson Difference Scheme for Solving a Type of Variable Coefficient Delay Partial Differential Equations

Table 1

Numerical results of (41) when ℎ=𝜏=1/100.

(𝑥,𝑡)	Numerical solution	Exact solution	|𝑢(𝑥𝑖,𝑡𝑘)−𝑢^𝑘𝑖|
(0.5,0.1)	0.667184	0.667184	2.501𝑒−007
(0.5,0.2)	0.727837	0.727837	4.324𝑒−007
(0.5,0.3)	0.788490	0.788490	5.702𝑒−007
(0.5,0.4)	0.849144	0.849143	6.812𝑒−007
(0.5,0.5)	0.909797	0.909796	7.753𝑒−007
(0.5,0.6)	0.970450	0.970449	8.586𝑒−007
(0.5,0.7)	1.031103	1.031102	9.347𝑒−007
(0.5,0.8)	1.091756	1.091755	1.006𝑒−006
(0.5,0.9)	1.152409	1.152408	1.074𝑒−006
(0.5,1.0)	1.213062	1.213061	1.140𝑒−006