Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems

Table 4

Comparison of exact solution 𝑦_exact, solution by variational iteration method 𝑦_VIM, and solutions by the wavelet-Galerkin method with quasilinearization technique 𝑦_NEW at second iteration, at different level of resolutions, and we used 𝐷8 as Galerkin bases.

			𝜆=0.5
Second iteration		𝐽=11	𝐽=13
𝑥	𝑦VIM [18]	𝑦NEW	𝑦NEW	𝑦exact
0.1	0.100042	0.095994	0.095956	0.095177
0.2	0.200334	0.192228	0.192152	0.190634
0.3	0.301128	0.288944	0.288829	0.286653
0.4	0.402677	0.386385	0.386231	0.383523
0.5	0.505241	0.484798	0.484606	0.481537
0.6	0.609082	0.584436	0.584204	0.581002
0.7	0.714470	0.685556	0.685284	0.682235
0.8	0.821682	0.788424	0.788112	0.785572
0.9	0.931008	0.893316	0.892962	0.891367
1.0	1.042740	1.000592	1.000194	1.000000