Boundary Value Problems

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

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)
0.2π	0.079548	0.079547	1.3155e − 06	0.079547	1.3155e − 06
0.4π	0.128712	0.128709	2.1285e − 06	0.128709	2.1285e − 06
0.6π	0.128712	0.128709	2.1285e − 06	0.128709	2.1285e − 06
0.8π	0.079548	0.079547	1.3155e − 06	0.079547	1.3155e − 06
Time		0.025744 s		2.695269 s

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