Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method

A numerical method for solving an axial dispersion model (two-point boundary value problem) with extremely high-order accuracy is presented. In this method, one first recasts fundamental differential equations into S-system (synergistic and saturable system) canonical form and then solves the resulting set of simultaneous first-order differential equations by the shooting method combined with a variable-order, variable-step Taylor series method. As a result, it is found that over wide ranges of systemic parameters (Peclet number, dimensionless kinetic constant, and reaction order), this method promises numerical solutions with the superhigh-order accuracy that is comparable to the machine accuracy of the computer used. The advantage of the numerical method is also discussed.