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Table 4 The approximate solution 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