Theory and Modern Applications
Table 4 The approximate solution ṽ at some grid points on \(t=1\) for Example 3
From: Implicit methods for the first derivative of the solution to heat equation
x | \(v^{2^{-5},2^{-13}} ( x,1 ) \) | \(v^{2^{-6},2^{-14}} ( x,1 ) \) | \(v^{2^{-7},2^{-15}} ( x,1 ) \) | \(v^{2^{-8},2^{-16}} ( x,1 ) \) |
|---|---|---|---|---|
0.125 | −0.88218321 | −0.88241771 | −0.88247701 | −0.88249191 |
0.25 | −0.77852029 | −0.77872997 | −0.77878291 | −0.77879622 |
0.375 | −0.68703982 | −0.68722539 | −0.68727216 | −0.68728390 |
0.5 | −0.60630576 | −0.60646779 | −0.60650853 | −0.60651874 |
0.625 | −0.53504253 | −0.53518148 | −0.53521631 | −0.53522502 |
0.75 | −0.47210904 | −0.47222525 | −0.47225424 | −0.47226147 |
0.875 | −0.41647280 | −0.41656648 | −0.41658968 | −0.41659545 |