Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm

Table 1

Numerical results for Troesch’s problem when 𝜆=0.5.

𝑥𝑖	Exact value	Approximate value	|Err(𝑥𝑖)|	|Res(𝑥𝑖)|
0	0	0	0	0
0.1	0.0951769020	0.0951768506	5.14476384×10^−8	4.33487462×10^−7
0.2	0.1906338691	0.1906337234	1.45741828×10^−7	9.77131143×10^−7
0.3	0.2866534030	0.2866533395	6.34609416×10^−8	4.75142679×10^−7
0.4	0.3835229288	0.3835228897	3.90866823×10^−8	3.31275728×10^−7
0.5	0.4815373854	0.4815373121	7.33121592×10^−8	6.41709009×10^−7
0.6	0.5810019749	0.5810019054	6.95247591×10^−8	8.39064329×10^−7
0.7	0.6822351326	0.6822350995	3.31330484×10^−8	8.13306207×10^−7
0.8	0.7855717867	0.7855717450	4.16561352×10^−8	6.07573447×10^−7
0.9	0.8913669875	0.8913669298	5.77267702×10^−8	2.24858269×10^−7
1	1	1	0	0