Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method

Table 1

Comparison of the absolute error 𝜀=1×10⁻³.

(𝑥,𝑡)	𝑢𝑇(𝑡,𝑥)	Approximate solution	Absolute error
(0.0001, 0.0001)	0.0001001	0.0001	1×10^−7
(0.0200, 0.0200)	0.0200200	0.0200	2×10^−5
(0.0050, 0.0050)	0.0050050	0.0050	5×10^−6
(0.8100, 0.8100)	0.8108100	0.8100	8×10^−4
(0.2000, 0.2000)	0.2002000	0.2000	2×10^−4
(0.5500, 0.5500)	0.5505500	0.5500	5×10^−4
(0.0330, 0.0330)	0.03303300	0.0330	3×10^−5
(1, 0)	1	1	0