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

Table 5

Comparison between exact solution and approximate solution of the new method of Experiment 2.

𝑥𝑖	𝑦𝑖	Exact solution	Approximate solution of the new method
0.0	0.0	1.000000000000000	1.000000001520331
0.0	.25	2.117000016612675	2.116999962177082
0.0	.5	4.481689070338065	4.481689131011527
0.0	.75	9.487735836358526	9.487735908103340
0.0	1	20.08553692318767	20.08553702346013
1	0.0	7.389056098930650	7.389056124466515
1	.25	15.64263188418817	15.64263190711622
1	.5	33.11545195869231	33.11545243577679
1	.75	70.10541234668786	70.10541228133020
1	1	148.4131591025766	148.4131603446419
.2	0.0	1.491824697641270	1.491824709011273
.2	1	29.96410004739701	29.96410038594428
.4	0.0	2.225540928492468	2.225540978673106
.4	1	44.70118449330082	44.70118489448246
.6	0.0	3.320116922736547	3.320116658933115
.6	1	66.68633104092514	66.68633190025831
.8	0.0	4.953032424395115	4.953032677031149
.8	1	99.48431564193381	99.48431532815737
.05	.05	1.284025416687741	1.284025760755220
.13	.26	2.829217014351560	2.829217082663191
.46	.16	4.055199966844675	4.055199961753327
.31	.42	6.553504862191149	6.553504821832245
.07	.58	6.553504862191149	6.553504889746486
.12	.73	11.35888208000146	11.35888287993308
.42	.91	35.51659315162847	35.51659237035928
.51	.57	15.33288701990720	15.33288705221003
.68	.82	45.60420832084874	45.60420881755932
.84	.37	16.28101980178843	16.28101996810631
.97	.68	53.51703422749116	53.51703410219755
.17	.93	22.87397954244081	22.87397949274820