Boundary Value Problems

Table 14 Numerical results of \(\mathrm{SP} _{3}\) at \(t=2\), with \({h_{x}}={h_{y}}= 0.01\pi \), \(\tau =0.005\)

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

(x,y)	Exact	R-ADI-CFDS4	Error 1	ADI-CFDS4	Error 2
(0.2π,0.2π)	0.006328	0.006328	5.2630e − 08	0.006328	5.2630e − 08
(0.4π,0.4π)	0.016567	0.016567	1.3779e − 07	0.016567	1.3779e − 07
(0.6π,0.6π)	0.016567	0.016567	1.3779e − 07	0.016567	1.3779e − 07
(0.8π,0.8π)	0.006328	0.006328	5.2630e − 08	0.006328	5.2630e − 08
Time		5.321289 s		1004.683564 s

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