This paper introduces two new numerical methods for integration of stiff ordinary differential equations. Following the idea of quantization based integration, i.e., replacing the time discretization by state quantization, the new methods perform first and second order backward approximations allowing to simulate stiff systems. It is shown that the new algorithms satisfy the same theoretical properties of previous quantization-based integration methods. The translation of the new algorithms into a discrete event (DEVS) specification and its implementation in a DEVS simulation tool is discussed. The efficience of the methods is illustrated comparing the simulation of two examples with the classic methods implemented by Matlab/Simulink.
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