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

x t HPSTM ADM Exact 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 1.0 0.1 0.4493037263 0.4493037263 0.4493289641