Table 1: Comparison study between HPSTM, ADM, and the exact solution when = 1.

x t HPSTMADMExact solution

0 0.1 1.221333333 1.221333333 1.221402758
0.2 0.1 0.9999431595 0.9999431595 1.000000000
0.4 0.1 0.8186842160 0.8186842160 0.8187307531
0.6 0.1 0.6702819447 0.6702819447 0.6703200460
0.8 0.1 0.5487804413 0.5487804413 0.5488116361
1.00.10.44930372630.44930372630.4493289641