A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Table 2

The numerical and exact solution of the test problem (32), where 𝑢₂(𝑡,𝑥) is exact solution and 𝑢^∗₂(𝑡,𝑥) is numerical solution, for 𝑥=0.1.

𝑡	𝑢2(𝑡,𝑥)	𝑢^∗2(𝑡,𝑥)	|𝑢2(𝑡,𝑥)−𝑢^∗2(𝑡,𝑥)|
0.1	−0.9949046649	−0.9949046653	0.0000000004
0.2	−0.9799685711	−0.9799685778	0.0000000067
0.3	−0.9552409555	−0.9552409875	0.0000000320
0.4	−0.9209688879	−0.9209689778	0.0000000899
0.5	−0.8774948036	−0.8774949653	0.0000001637
0.6	−0.8252530813	−0.8252532000	0.0000001187
0.7	−0.7647657031	−0.7647652653	0.0000004378
0.8	−0.6966370386	−0.6966345778	0.0000024608
0.9	−0.6215478073	−0.6215398875	0.0000079198
1.0	−0.5402482757	−0.5402277778	0.0000204979