THREE-STEP HYBRID BLOCK METHODS FOR SOLVING FIRST-ORDER LINEAR AND NONLINEAR SYSTEMS

Abstract

For first-order systems that are either linear or nonlinear, this study derives two three-step hybrid
block approaches. Applying the collocation and interpolation approach, with power series as the
basis function, allows for the derivation to be carried out. By include a single off-grid point and two
off-grid points inside the three-step integration interval, respectively, the first and second three-step
hybrid block approaches are generated. To evaluate their accuracy and efficiency, the obtained
techniques were used to certain linear and nonlinear first-order systems.Based on the outcomes, it is
clear that the three-step hybrid block technique including two off-grid spots outperformed its one-
off-grid counterpart. We also found that the two derived approaches outperformed the current
methods we compared them against. This was evident from the findings. We dug further into the
fundamental features of the obtained approaches. The zero-stability, consistence, convergence, and
absolute stability regions are all characteristics that fall under this category.