A Review of Some Recent Results for the Approximate Analytical Solutions of Nonlinear Differential Equations

Table 1

Numerical results (in t direction) for |𝑢(𝑥,𝑡)−𝜙₃₀(𝑥,𝑡)| where 𝑢(𝑥,𝑡)=𝑒^{(1−𝜋2)𝑡}cos(𝜋𝑥) for (3.12)–(3.14).

𝑡𝑖∣𝑥𝑖	0.1	0.2	0.3	0.4	0.5
0.1	1.9942𝐸−21	1.6973𝐸−21	1.2322𝐸−21	6.4790𝐸−22	0.0000𝐸+00
0.2	4.3765𝐸−20	3.7228𝐸−20	2.7048𝐸−20	1.4220𝐸−20	0.0000𝐸+00
0.3	8.5955𝐸−20	7.3116𝐸−20	5.3123𝐸−20	2.7928𝐸−20	0.0000𝐸+00
0.4	1.0148𝐸−16	8.6329𝐸−17	6.2722𝐸−17	3.2975𝐸−17	0.0000𝐸+00
0.5	7.9889𝐸−14	6.7958𝐸−14	4.9374𝐸−14	2.5957𝐸−14	0.0000𝐸+00