On Some Advantages of the Predictor-Corrector Methods

Usually, all numerical methods are divided into two sets known as explicit and implicit methods. Explicit methods (EM) are used to find a solution to a problem directly, without requiring initial preparation. But when using the implicit method (IM), other methods can sometimes be employed. Implicit methods are known to be more accurate than explicit ones. Therefore, the question arises about finding the golden mean. To accomplish this, we utilize certain properties of the predictor and corrector methods. We take into account that in forecasting methods, we use EM. However, I will show here that in some cases, IMs can be used as correction methods. It is clear that the results obtained here are fully consistent with the theoretical ones. To address the aforementioned issues, we employ the initial value problem (IVP) for a first-order ordinary differential equation (ODE). Conventional methods compare various nanomaterials (NMs) using multi-step, extended, and hybrid approaches.