Numerical Treatment by Using a Hybrid Efficient Technique for the Biochemical Reaction Model
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In this article, we implement a spectral collocation method by using the properties of Legendre and Lagrange polynomials for solving the resulting nonlinear system of ODEs of the biochemical reaction model. This technique reduces the proposed model to a system of algebraic equations. We prove the uniqueness and present the local stability of the given model. A comparison with the numerical solution is obtained by using the RK4 method and the previously published results using the Picard-Padè method. The proposed method introduces a promising tool for solving many nonlinear systems of differential equations. Numerical illustrations are stated to demonstrate utility, validity and the great potential of the introduced method.
KeywordsBiochemical reaction model Spectral collocation method Legendre–Lagrange Polynomials RK4 method Stability analysis
Mathematics Subject Classification65N12 41A30
The author thanks Deanship of Academic Research, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA, for the Financial support of the project number (371204).
- 6.Khader, M.M.: On the numerical solutions to nonlinear biochemical reaction model using Picard–Padé technique. World J. Model. Simul. 9(1), 38–46 (2013)Google Scholar
- 8.Kumar, R., Kumar, S.: A new fractional modelling on susceptible-infected-recovered equations with constant vaccination rate. Nonlinear Eng. 3(1), 11–19 (2013)Google Scholar
- 10.Matignon, D.: Stability results for fractional differential equations with applications to control processing. Computational engineering in systems and application. In: Multiconference, IMACS, IEEE-SMC, Lille, France, vol. 2, pp. 963–968 (1996)Google Scholar