Numerical Solution of Poisson's Equation Using a Combination of Logarithmic and Multiquadric Radial Basis Function Networks

Table 3

Comparison between exact solution and approximate solution of IRBFN method on the polar coordinate of Experiment 1 [17].

𝑥𝑖	𝑦𝑖	Exact solution	Approximate solution of IRBFN method on the polar coordinate	Error of IRBFN method on the polar coordinate
0.3333	0.2	0.4070935392947847	0.407093539278427	1.64×10^−11
0.3333	0.4	0.4972251717238353	0.497225171776793	5.29×10^−11
0.3333	0.6	0.6073121961701566	0.607919812163175	3.95×10^−11
0.3333	0.8	0.7417727914665396	0.741772791449410	1.71×10^−11
0.6667	0.2	0.8143092188653853	0.814309218844426	2.09×10^−11
0.6667	0.4	0.9945995259174347	0.994599525931543	1.41×10^−11
0.6667	0.6	1.214806604220352	1.214806604225190	4.84×10^−12
0.6667	0.8	1.483768137025928	1.483768136992937	3.30×10^−11
1.0000	0.2	1.221402758160170	1.221402758117891	4.23×10^−11
1.0000	0.4	1.491824697641270	1.491824697612953	2.83×10^−11
1.0000	0.6	1.822118800390509	1.822118800390206	3.03×10^−11
1.0000	0.8	2.225540928492468	2.225540928445109	4.74×10^−11
1.3333	0.2	1.628496297454955	1.628496297401382	5.37×10^−11
1.3333	0.4	1.989049869365105	1.989049869316768	4.84×10^−11
1.3333	0.6	2.429430996560666	2.429430996510109	5.06×10^−11
1.3333	0.8	2.967313719959008	2.967313719902712	5.63×10^−11
1.6666	0.2	2.035589836749739	2.035711976964034	6.16×10^−11
1.6666	0.4	2.486275041088941	2.486424223498127	6.06×10^−11
1.6666	0.6	3.036743192730822	3.036925404550813	6.01×10^−11
1.6666	0.8	3.709086511425547	3.709309065459067	5.94×10^−11