Solution of a two-point boundary value model of immobilized enzyme reactions, using an S-system-based root-finding method
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摘要
The analysis of immobilized enzyme reactions leads to a two-point boundary value problem that requires numerical solutions based on root-finding methods. The standard Newton–Raphson (N–R) algorithm is adequate if the root-finding is initiated close to the true solution; in other cases, large numbers of iterations may be needed before the algorithm converges. An alternative is a root-finding method based on the theory of S-systems. This method turns out to be much more robust and efficient than the N–R algorithm. It converges quadratically, with fewer iterations, and in a wider range of relevant initial values. An investigation of a simpler algebraic equation with a similar mathematical structure demonstrates that the rate of convergence in the S-system method is not very sensitive to the distance between the root and initial value, whereas convergence of the N–R algorithm slows down drastically with increasing distance.
论文关键词:Immobilized enzyme reaction,Two-point boundary value problem,Newton–Raphson method,S-system,Biochemical Systems Theory,Taylor-series method,Shooting method
论文评审过程:Available online 31 January 2002.
论文官网地址:https://doi.org/10.1016/S0096-3003(01)00008-X