Cubic Spline Method for 1D Wave Equation in Polar Coordinates

Table 1

𝜆=𝑘/ℎ=0.8, 𝑡=5.0.

h	Proposed 𝑂(𝑘^2+ℎ^4) method		𝑂(𝑘^2+ℎ^2) method
	𝛼=1	𝛼=2	𝛼=1	𝛼=2
1/16	0.6222 (−4)	0.3981 (−4)	0.2094 (−3)	0.2760 (−3)
1/32	0.1593 (−4)	0.1057 (−4)	0.5404 (−4)	0.6849 (−4)
1/64	0.3997 (−5)	0.2699 (−5)	0.1365 (−4)	0.1705 (−4)
1/128	0.9944 (−6)	0.6797 (−6)	0.3412 (−5)	0.4257 (−5)