An Improved Numerical Method for the Simulation of Nonlinear Systems

Because the models that arise from the bioindustry are highly nonlinear, in order to simulate them we propose an adaptive PID control of step-size, where the variation of the step-size is proportional to the error criterion and a digital filter is used in order to smoothen up the step-size variation. The present paper compares this numerical method with a wide selection of numerical methods that can be used in order to simulate the evolution of the systems. Although the application is designed with the purpose of simulating the evolution of mathematical models that arise from the food processing industry, it can also be used for models that come from other areas of the industry. The proposed numerical method is tested and validated by using some nonlinear models of classical systems such as Lorenz and Van der Pol, but also nonlinear models of bioprocesses.