Numerical Solution to Nonlinear Biochemical Reaction Model Using Hybrid Polynomial Basis Differential Evolution Technique

In this paper, we present an approximate numerical solution to the well known Michaelis-Menten nonlinear biochemical reaction system using a stochastic technique based on hybrid polynomial basis evolutionary computing. The approximate solution is expanded as a linear combination of polynomial basis with unknown parameters. The system of nonlinear differential equation is transformed into an equivalent global error minimization problem. A trial solution is formulated using a fitness function with unknown parameters. Two popular evolutionary algorithms such as Genetic algorithm (GA) and Differential evolution (DE) are used to solve the minimization problem and to obtain the unknown parameters. The effectiveness of the proposed technique is demonstrated in contrast with fourth-order Runge Kutta method (RK-4) and some well known standard methods including homotopy perturbation method (HPM), variational iteration method (VIM), differential transform method (DTM), and modified Picard iteration method (Picard-Pade). The comparisons of numerical results validate the efficacy and viability of the suggested technique. The results are found to be in sharp agreement with RK-4 compared to some popular standard methods.

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