Computational Method for the Simulation of Duffing Oscillators

Hybrid-Block Method for the Solution of Second Order Non-linear Differential Equations

“…For the intent of application of the novel hybrid block technique, we have analyzed and studied four numerical examples. The findings shown in Tables 1 through 4 made it abundantly evident that the newly developed hybrid block approach functioned brilliantly in contrast to the methods described in [6,7] and [27]. The comparison was established since both authors handled the same problems, and the order of the method in [27] is equal to the order in our new method.…”

“…The findings shown in Tables 1 through 4 made it abundantly evident that the newly developed hybrid block approach functioned brilliantly in contrast to the methods described in [6,7] and [27]. The comparison was established since both authors handled the same problems, and the order of the method in [27] is equal to the order in our new method. The difference in error between our new method and the methods proposed by [6,7] and [27,28] is also less according to the implementation of our new method.…”

“…The comparison was established since both authors handled the same problems, and the order of the method in [27] is equal to the order in our new method. The difference in error between our new method and the methods proposed by [6,7] and [27,28] is also less according to the implementation of our new method. The convergence of our numerical method may be seen graphically in each of the four examples' graphs.…”

“…We shall use "EDM" to mean error in our new derived method. The exact solution is given by Source [6], [27] The exact solution is given by, .…”