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

Table 7

Comparison between exact solution and approximate solution of the new method of Experiment 3.

𝑥𝑖	𝑦𝑖	Exact solution	Approximate solution of the new method	Error of the new method
0.0	0.5	38.87195121951220	38.87195121952383	1.16×10^−11
0.0	1.5	37.65243902439024	37.65243902440016	9.92×10^−12
0.0	3.5	31.55487804878049	31.55487804879181	1.13×10^−11
0.0	5.5	20.57926829268293	20.57926829269648	1.35×10^−11
0.0	7.5	4.72560975609756	4.72560975611862	2.11×10^−11
2.0	0.0	37.46341463414634	37.46341463417008	2.37×10^−11
4.0	0.0	32.78048780487805	32.78048780491504	3.70×10^−11
6.0	0.0	24.97560975609756	24.97560975615097	5.34×10^−11
8.0	0.0	14.04878048780488	14.04878048786474	5.99×10^−11
10.0	0.0	0.00000000000000	0.00000000005427	5.43×10^−11
2.0	1.6	35.90243902439024	35.90243902440453	1.43×10^−11
4.0	1.6	31.21951219512195	31.21951219515048	2.85×10^−11
6.0	1.6	23.41463414634146	23.41463414638886	4.74×10^−11
8.0	1.6	12.48780487804878	12.48780487810293	5.41×10^−11
2.0	4.0	27.70731707317073	27.70731707318550	1.48×10^−11
4.0	4.0	23.02439024390244	23.02439024392700	2.46×10^−11
6.0	4.0	15.21951219512195	15.21951219516124	3.93×10^−11
8.0	4.0	4.292682926829268	4.29268292687660	4.73×10^−11
2.0	5.6	18.34146341463414	18.34146341465220	1.81×10^−11
4.0	5.6	13.65853658536585	13.65853658539350	2.76×10^−11
6.0	5.6	5.85365853658536	5.85365853662464	3.93×10^−11
9.798	1.6	−0.00031375609756	−0.00031375604674	5.08×10^−11
8.660	4.0	0.00171707317073	0.00171707321643	4.57×10^−11
7.141	5.6	0.00238790243902	0.00238790247911	4.01×10^−11
2.0	7.838	0.00350975609756	0.00350975612416	2.66×10^−11
4.0	7.332	0.00108292682927	0.00108292685914	2.99×10^−11
6.0	6.4	0.00000000000000	0.00000000003483	3.48×10^−11
8.0	4.8	0.00000000000000	0.00000000004390	4.39×10^−11