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This work concerns the application of the homotopy method to solve the mathematical model of a non-adiabatic chemical continuous stirred tank reactor (CSTR) and tubular reactor with mass recycle (TRR) (Berezowski 2000. Spatio-temporal chaos in tubular chemical reactors with the recycle of mass,  Chaos, Solitons &amp; Fractals , vol. 11, no. 8, pp. 1197–1204). This method was associated with the parametric multivariable continuation algorithm. Thanks to this, this method can automatically find all the multiple steady states of the reactor model without the need to use any iteration. The parametric continuation method is used to determine a curve whose each point is a solution of the tested model. Therefore, the starting point must be very precisely designated so that it lies on this curve. Otherwise, the result is a graph that deviates from the correct graph. However, this condition is not required when the homotopy method is also introduced into the calculations. The starting point can then be a point with any coordinates. Different curves are also obtained, but the homotopy method ensures that each of them passes through the point where the parameter  p  = 1. The solution we are looking for in the model is just such a point. This is undoubtedly a big advantage resulting from the combination of both above-mentioned methods.

Determination of steady states of tank and recycle tubular reactors using homotopy and parametric continuation methods