An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method

Table 4

Numerical solution of Troesch's problem for 𝜆=10.

𝑡	Present method	B-spline, 𝑁=790	𝑦1750(𝑥)	𝑦14(𝑥)=𝜇tanh^−1(𝜇1(𝑥))	𝑦24(𝑥)=𝜇tanh^−1(𝜇2(𝑥))
	𝑀=20,𝑘=5	[10]	[12]	[13]	[13]
0.00	0	0	0	0	0
0.100	4.2110×10^−5	4.2097×10^−5	4.2113×10^−5	4.2112×10^−5	4.2112×10^−5
0.200	1.2996×10^−4	1.2992×10^−4	1.2997×10^−4	1.2996×10^−4	1.2996×10^−4
0.300	3.5896×10^−4	3.5886×10^−4	3.5899×10^−4	3.5898×10^−4	3.5898×10^−4
0.400	9.7785×10^−4	9.7762×10^−4	9.7792×10^−4	9.7790×10^−4	9.7790×10^−4
0.500	2.6589×10^−3	2.6583×10^−3	2.6591×10^−3	2.6590×10^−3	2.6590×10^−3
0.600	7.2286×10^−3	7.2272×10^−3	7.2291×10^−3	7.2289×10^−3	7.2289×10^−3
0.700	1.9663×10^−2	1.9660×10^−2	1.9664×10^−2	1.9664×10^−2	1.9664×10^−2
0.800	5.3728×10^−2	5.3720×10^−2	5.3732×10^−2	5.3730×10^−2	5.3730×10^−2
0.900	1.5210×10^−1	1.5209×10^−1	1.5212×10^−1	1.5211×10^−1	1.5211×10^−1
0.925	2.0199×10^−1	2.0199×10^−1	2.0201×10^−1	2.0201×10^−1	2.0201×10^−1
0.950	2.7625×10^−1	2.7623×10^−1	2.7628×10^−1	2.7627×10^−1	2.7627×10^−1
0.970	3.7224×10^−1	3.7223×10^−1	3.7229×10^−1	3.7226×10^−1	3.7226×10^−1
0.980	4.4822×10^−1	4.4820×10^−1	4.4825×10^−1	4.4823×10^−1	4.4823×10^−1
0.990	5.7407×10^−1	5.7405×10^−1	5.7411×10^−1	5.7408×10^−1	5.7408×10^−1
0.995	6.9011×10^−1	6.9010×10^−1	6.9018×10^−1	6.9011×10^−1	6.9011×10^−1
0.997	7.6577×10^−1	7.6576×10^−1	7.6587×10^−1	7.6577×10^−1	7.6577×10^−1
0.998	8.1802×10^−1	8.1802×10^−1	8.1816×10^−1	8.1803×10^−1	8.1803×10^−1
0.999	8.8899×10^−1	8.8899×10^−1	8.8917×10^−1	8.8899×10^−1	8.8899×10^−1
1.000	1.0000	1.0000	1.0000	9.9999	9.9999