Implementation and Experimental Comparison of EFORK3, M2sFRK, and Grünwald–Letnikov on STM32 Microcontrollers with Floating- and Fixed-Point Arithmetic

This study compares EFORK3, the implemented memoryless two-stage recurrence (M2sFRK), and the finite-memory Grünwald–Letnikov (GL) method on STM32 microcontrollers across the Chen, Liu, and Hammouch–Mekkaoui systems, the STM32F746 and STM32H755, and floating- or fixed-point arithmetic. A full-history Caputo Adams–Bashforth–Moulton (ABM) solution whose numerical accuracy was assessed through step size refinement provides the numerical reference; the C numerical routines were evaluated through short-horizon comparisons, independent bit-exact fixed-point checks, and release-build acceptance tests. Physical timing and dense trajectory measurements characterized the solver call cost and reconstructed finite-time dynamics, yielding positive largest-exponent estimates; matched F746 and H755 captures were bit-identical. M2sFRK bitstreams were evaluated with NIST SP 800-22, PractRand, and TestU01, and the findings varied by system and arithmetic representation; under some fixed-point conditions, distinct initial conditions produced identical sequences. Overall, the implemented M2sFRK recurrence required the fewest cycles and least static RAM but does not generally approximate the same Caputo initial-value problem for 0