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

Table 1

The numerical and exact solution of the test problem (32), where 𝑢₁(𝑡,𝑥) is the exact solution and 𝑢^∗₁(𝑡,𝑥) is the numerical solution, for 𝑥=0.1.

𝑡	𝑢1(𝑡,𝑥)	𝑢^∗1(𝑡,𝑥)	|𝑢1(𝑡,𝑥)−𝑢^∗1(𝑡,𝑥)|
0.1	−0.0895789043	−0.0895789043	0
0.2	−0.0810543445	−0.0810543422	0.0000000023
0.3	−0.0733410038	−0.0733409887	0.0000000151
0.4	−0.0663616845	−0.0663616355	0.0000000490
0.5	−0.0600465353	−0.0600464409	0.0000000944
0.6	−0.0543323519	−0.0543322800	0.0000000719
0.7	−0.0491619450	−0.0491621943	0.0000002493
0.8	−0.0444835674	−0.0444849422	0.0000013748
0.9	−0.0402503963	−0.0402546487	0.0000042524
1.0	−0.0364200646	−0.0364305555	0.0000104909