The numerical solution of partial differential-algebraic equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Comparison of the numerical solution of $u_{1} (x, t)$ with exact solutions ( $t = 0.01$ )

x	$u_{1} (x, t)$	$r_{4, 3} (x, t)$	$\| u_{1} (x, t) - r_{4, 3} (x, t) \|$
−0.5	0.2475124584	0.2475124584	0
−0.4	0.1584079734	0.1584079734	0
−0.3	0.08910448503	0.08910448502	1.10⁻¹¹
−0.2	0.03960199335	0.03960199334	1.10⁻¹¹
−0.1	0.009900498337	0.009900498336	1.10⁻¹²
0.1	0.009900498337	0.009900498336	1.10⁻¹²
0.2	0.03960199335	0.03960199334	1.10⁻¹¹
0.3	0.08910448503	0.08910448502	1.10⁻¹¹
0.4	0.1584079734	0.1584079734	0
0.5	0.2475124584	0.2475124584	0