Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation

Table 2

𝐿₂-norm error ‖𝑢_𝑒(𝑥,𝑡)−𝑢_𝑎(𝑥,𝑡)‖₂, maximum absolute error, and maximum relative error at the times 𝑡= 0.25, 0.50, 0.75, and 1.

𝑡	‖𝑢𝑒(𝑥,𝑡)−𝑢𝑎(𝑥,𝑡)‖2	Maximum absolute error	Maximum relative error
0.25	0.001934504062	0.00002345900000	0.00001529179356
0.5	0.002320886866	0.00003255400000	0.00001515040617
0.75	0.002486049062	0.00003626700000	0.00001264980809
1	0.002172409395	0.00002491464924	0.00000670058118