Zero-stable Multistep formulas with equally spaced off-grid points for second-order differential equations: Derivation and Analysis

This paper focuses on using zero-stable multistep formulae with evenly spaced off-grid points to numerically simulate differential equations originating from applied mathematics and engineering. The new multistep formulae used the differential system's collocation and power series interpolation as an approximated solution. In order to concurrently provide numerical solutions for the problems under consideration, the primary integrator and its auxiliary integrators are combined and applied. The integrators' theoretical analysis was examined and determined to be consistent with the current linear multistep method theorem. The techniques’s theoretical analysis were determined such as the order and error constants, consistency, zero-stability, convergency and the stability were also determined. The numerical outcomes of the techniques’s analysis contrasted with those of a few previously used techniques. The findings showed that the approach would provides greater accuracy than several other approaches already in use in the literature, making it a significant improvement over those approaches.