Computed solutions of Problems 1 and 2 at
(a) Problem 1
x | Exact | FSFD | HSFD |
---|---|---|---|
0 | 0.288675135 | 0.288675135 | 0.288675135 |
0.0625 | 0.306717331 | 0.306749721 | 0.306749714 |
0.125 | 0.324759526 | 0.324813673 | 0.324813662 |
0.1875 | 0.342801722 | 0.342870180 | 0.342870166 |
0.25 | 0.360843918 | 0.360921285 | 0.360921270 |
0.3125 | 0.378886114 | 0.378968320 | 0.378968307 |
0.375 | 0.396928310 | 0.397012168 | 0.397012156 |
0.4375 | 0.414970506 | 0.415053423 | 0.415053413 |
0.5 | 0.433012702 | 0.433092496 | 0.433092487 |
0.5625 | 0.451054898 | 0.451129678 | 0.451129671 |
0.625 | 0.469097094 | 0.469165183 | 0.469165178 |
0.6875 | 0.487139290 | 0.487199174 | 0.487199170 |
0.75 | 0.505181486 | 0.505231780 | 0.505231778 |
0.8125 | 0.523223681 | 0.523263108 | 0.523263107 |
0.875 | 0.541265877 | 0.541293248 | 0.541293247 |
0.9375 | 0.559308073 | 0.559322278 | 0.559322277 |
1 | 0.577350269 | 0.577350269 | 0.577350269 |
(b) Problem 2
x | Exact | FSFD | HSFD |
---|---|---|---|
0 | 0.902587365 | 0.902587365 | 0.902587365 |
0.0625 | 0.886920140 | 0.886921108 | 0.886921025 |
0.125 | 0.872041440 | 0.872043136 | 0.872042992 |
0.1875 | 0.857887266 | 0.857889487 | 0.857889302 |
0.25 | 0.844400662 | 0.844403238 | 0.844403027 |
0.3125 | 0.831530750 | 0.831533538 | 0.831533312 |
0.375 | 0.819231921 | 0.819234798 | 0.819234569 |
0.4375 | 0.807463151 | 0.807466014 | 0.807465789 |
0.5 | 0.796187429 | 0.796190189 | 0.796189976 |
0.5625 | 0.785371262 | 0.785373844 | 0.785373649 |
0.625 | 0.774984258 | 0.774986600 | 0.774986426 |
0.6875 | 0.764998769 | 0.765000814 | 0.765000665 |
0.75 | 0.755389575 | 0.755391278 | 0.755391156 |
0.8125 | 0.746133620 | 0.746134943 | 0.746134850 |
0.875 | 0.737209781 | 0.737210690 | 0.737210627 |
0.9375 | 0.728598659 | 0.728599125 | 0.728599093 |
1 | 0.720282406 | 0.720282406 | 0.720282406 |