Developing and Implementing Two-Step Adams-Bashforth-Moulton Method with Variable Stepsize for the Simulation Tool DynStar

The simulation tool DynStar, created by Hochschule Zittau/Görlitz IPM department, was previously using only single-step methods to solve differential equations.This paper describes the development of a multiple step method to complement the others.The Introduction gives the reader a better idea why a multiple step method can be useful.The theory part is focused on the two-step Adams-Bashforth-Moulton method and how it is possible to make the formulas suitable for variable stepsize.Further, an algorithm is developed to solve the differential equations, using the ABM formulas and adjusting the stepsize according to the error between the prediction and the correction.This is described in the Implementation section.Finally, the performance of the ABM method is compared with RK4 and the Hanna method in the Results section.