Novel approach for solving higher-order differential equations with applications to the Van der Pol and Van der Pol–Duffing equations

Beni-Suef University Journal of Basic and Applied Sciences

Table 7 Comparison of Van der Pol–Duffing oscillator response obtained by different techniques and their relative errors compared to RK4. \(\varepsilon = - \mu = 0.2, F = 0.53\), \(\omega = 1\), \(y\left( {t_{0} } \right) = 0.1\) and \(\dot{y}\left( {t_{0} } \right) = - 0.2\)

t	36	38	40	42	44	46	48	50	Σerror
Present	− 0.938	0.344	0.975	− 1.861	2.128	− 1.483	0.080	1.372
ode15s	− 0.259	1.345	− 1.560	− 0.240	1.756	− 0.059	− 1.416	1.614
ode45	− 1.338	0.498	0.614	− 1.398	1.964	− 1.632	0.001	1.599
RK4	− 1.036	1.081	0.113	− 0.990	1.812	− 1.426	− 0.264	1.688
erropres	9	68	761	88	17	4	130	19	1842
errode15s	75	24	1478	76	3	96	437	4	3322
errode45	29	54	442	41	8	14	100	5	2324