TY - JOUR
T1 - Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method
AU - Shiraishi, F.
PY - 2001/8/15
Y1 - 2001/8/15
N2 - 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.
AB - 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.
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U2 - 10.1016/S1385-8947(00)00252-7
DO - 10.1016/S1385-8947(00)00252-7
M3 - Article
AN - SCOPUS:0035880281
VL - 83
SP - 175
EP - 183
JO - Chemical Engineering Journal
JF - Chemical Engineering Journal
SN - 1385-8947
IS - 3
ER -