Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics
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 num...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2020-09-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/1366 |
| _version_ | 1797724260200873984 |
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| author | John J. H. Miller Eugene O'Riordan |
| author_facet | John J. H. Miller Eugene O'Riordan |
| author_sort | John J. H. Miller |
| collection | DOAJ |
| description | 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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| first_indexed | 2024-03-12T10:14:47Z |
| format | Article |
| id | doaj.art-721ff393b03543ab8ca3716a93bd4901 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T10:14:47Z |
| publishDate | 2020-09-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-721ff393b03543ab8ca3716a93bd49012023-09-02T10:36:14ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182020-09-019210.11145/j.biomath.2020.08.227858Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kineticsJohn J. H. MillerEugene O'RiordanA 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. ?http://www.biomathforum.org/biomath/index.php/biomath/article/view/1366enzyme-substrate dynamics, nonlinear system, shishkin mesh, parameter-uniform convergence |
| spellingShingle | John J. H. Miller Eugene O'Riordan Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics Biomath enzyme-substrate dynamics, nonlinear system, shishkin mesh, parameter-uniform convergence |
| title | Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| title_full | Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| title_fullStr | Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| title_full_unstemmed | Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| title_short | Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| title_sort | robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics |
| topic | enzyme-substrate dynamics, nonlinear system, shishkin mesh, parameter-uniform convergence |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/1366 |
| work_keys_str_mv | AT johnjhmiller robustnumericalmethodforasingularlyperturbedproblemarisinginthemodellingofenzymekinetics AT eugeneoriordan robustnumericalmethodforasingularlyperturbedproblemarisinginthemodellingofenzymekinetics |