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 boundar y value problem) with extremely high-order accuracy is presented. In this m ethod, one first recasts fundamental differential equations into S-system ( synergistic and saturable system) canonical form and then solves the result ing 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 (Pecl et number, dimensionless kinetic constant, and reaction order), this method promises numerical solutions with the superhigh-order accuracy that is com parable to the machine accuracy of the computer used. The advantage of the numerical method is also discussed. (C) 2001 Elsevier Science B.V. All righ ts reserved.