Theory and Modern Applications
Table 4 Comparison of exact and numerical solutions for Example 4.2, \(M=20\)
x | exact solution | CBS-FEM | LBS-FEM | error(CBS-FEM) | error(LBS-FEM) |
|---|---|---|---|---|---|
0.1 | 0.099666 + i0.010000 | 0.100291 + i0.009703 | 0.100194 + i0.010499 | 0.000691 | 0.000726 |
0.2 | 0.197323 + i0.039999 | 0.197895 + i0.039802 | 0.197735 + i0.040591 | 0.000605 | 0.000721 |
0.3 | 0.290919 + i0.089992 | 0.290960 + i0.089624 | 0.390736 + i0.090365 | 0.000369 | 0.000416 |
0.4 | 0.378328 + i0.159954 | 0.377536 + i0.159159 | 0.377240 + i0.159896 | 0.001121 | 0.001089 |
0.5 | 0.457304 + i0.249826 | 0.455567 + i0.248503 | 0.455192 + i0.249227 | 0.002182 | 0.002195 |
0.6 | 0.525453 + i0.359482 | 0.522883 + i0.357628 | 0.522414 + i0.358351 | 0.003167 | 0.003242 |
0.7 | 0.580197 + i0.488693 | 0.577145 + i0.486461 | 0.576579 + i0.487178 | 0.003780 | 0.003921 |
0.8 | 0.618749 + i0.637088 | 0.615928 + i0.634747 | 0.615200 + i0.635499 | 0.003665 | 0.003888 |
0.9 | 0.638093 + i0.804098 | 0.636498 + i0.802167 | 0.635610 + i0.802937 | 0.002503 | 0.002740 |