Boundary Value Problems

Table 6 Numerical results of \(\mathrm{SP} _{2}\) at \(t = 1\), with \(h=0.02\), \(\tau =0.01\)

From: A reduced fourth-order compact difference scheme based on a proper orthogonal decomposition technique for parabolic equations

x	Exact	R-CFDS4	Error (R-CFDS4)	CFDS4	Error (CFDS4)
0.2	0.552561	0.552561	2.2473e − 07	0.552561	2.2473e − 07
0.4	0.660730	0.660730	3.0933e − 07	0.660730	3.0933e − 07
0.6	0.792848	0.792847	3.8266e − 07	0.792847	3.8266e − 07
0.8	0.954216	0.954216	4.6805e − 07	0.954216	4.6805e − 07
Time		0.013232 s		4.530407 s

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