Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics


  • John J. H. Miller
  • Eugene O'Riordan



Enzyme-substrate dynamics, nonlinear system, Shishkin mesh, parameter-uniform convergence


A system of two coupled nonlinear initial value equations, arising in the mathematical modelling of enzyme kinetics, is examined. The system is singularly perturbed and one of the components will contain steep gradients. A priori parameter explicit bounds on the two components are established. A numerical method incorporating a specially constructed piecewise-uniform mesh is used to generate numerical approximations, which are shown to converge pointwise to the continuous solution irrespective of the size of the singular perturbation parameter. Numerical results are presented to illustrate the computational performance of the numerical method. The numerical method is also remarkably simple to implement.


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