Fixed-Point Implementation of Extrapolation ODE Solvers

In this paper we propose the fixed-point implementation of extrapolation ODE solvers with adaptive stepsize. We show the applicability of the given approach for solving nonlinear differential equations through the simulation of the chaotic Halvorsen system. The experimental part of the study considers the analysis of local truncation error and integration step variation for floating-point and fixed-point solvers with different machine word length. It is revealed that with equal parameters fixed-point ODE solvers can achieve greater accuracy than floating-point solvers for the same bit length.