A Meshless Method for the Numerical Solution of a Two-Dimension IHCP

Table 8

Error and RMS errors for 𝑈(𝑥,𝑦,𝑡) and 𝑔₀(𝑦,𝑡) on the intervals 𝑥∈[0,0.1], 𝑦∈[0,1], and 𝑡∈[0,1] for Example  2.

Method	Error	𝑁=𝑀=𝑆=3	𝑁=6,𝑀=4,𝑆=5	𝑁=𝑀=𝑆=5	𝑁=5,𝑀=6,𝑆=5
GA-RBFs; (𝑐=0.1)	RMS(𝑈)	1.801𝐸−3	3.298𝐸−5	2.040𝐸−5	1.092𝐸−5
	Error (𝑈)	4.237𝐸−3	8.186𝐸−5	5.112𝐸−5	4.281𝐸−5
	RMS(𝑔0)	2.797𝐸−3	5.222𝐸−5	3.349𝐸−5	1.438𝐸−5
	Error (𝑔0)	7.066𝐸−3	1.397𝐸−4	9.055𝐸−5	7.367𝐸−4
IMQ-RBFs; (𝑐=50)	RMS(𝑈)	1.507𝐸−3	5.384𝐸−4	2.137𝐸−4	1.560𝐸−4
	Error (𝑈)	3.546𝐸−3	1.336𝐸−3	5.354𝐸−4	3.931𝐸−4
	RMS(𝑔0)	2.336𝐸−3	8.666𝐸−4	3.507𝐸−4	2.562𝐸−4
	Error (𝑔0)	5.902𝐸−3	2.318𝐸−3	9.491𝐸−4	6.982𝐸−4
MQ-RBFs; (𝑐=50)	RMS(𝑈)	1.379𝐸−3	5.107𝐸−4	1.634𝐸−4	1.343𝐸−4
	Error (𝑈)	3.243𝐸−3	1.267𝐸−3	4.094𝐸−4	3.382𝐸−4
	RMS(𝑔0)	2.136𝐸−3	8.221𝐸−4	2.682𝐸−4	2.220𝐸−4
	Error (𝑔0)	5.398𝐸−3	2.199𝐸−3	7.257𝐸−4	6.004𝐸−4
IQ-RBFs; (𝑐=50)	RMS(𝑈)	1.565𝐸−3	3.116𝐸−4	1.172𝐸−4	1.342𝐸−5
	Error (𝑈)	3.683𝐸−3	7.736𝐸−4	2.951𝐸−4	2.383𝐸−4
	RMS(𝑔0)	2.426𝐸−3	5.013𝐸−4	2.913𝐸−4	2.205𝐸−4
	Error (𝑔0)	6.130𝐸−3	1.341𝐸−3	6.371𝐸−4	6.008𝐸−4