Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

Table 4

Value of the root of mean square of residual errors that is computed by (29). The results for Examples 1, 2, and 3 are reported for Gaussian radial basis functions and . Comparison between Tables 1, 2, and 3 and following results confirms the strong correlation between absolute maximum of error and the root of mean square of residual errors. In brief, the estimation error of approximation is possible by (29) even as the exact solution is not given.

	Example 1	Example 2	Example 3
4	1.0  ×	9.3  ×	1.2  ×
9	1.8  ×	8.9  ×	2.1  ×
16	1.8  ×	1.4  ×	8.3  ×
25	1.4  ×	3.1  ×	7.5  ×
36	8.5  ×	2.0  ×	5.9  ×
49	6.8  ×	5.2  ×	8.2  ×