1. The multistage homotopy analysis method: application to a biochemical reaction model of fractional order.
- Author
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Zurigat, Mohammad, Momani, Shaher, and Alawneh, Ahmad
- Subjects
HOMOTOPY theory ,BIOREACTORS ,FRACTIONAL calculus ,MATHEMATICAL models ,ENZYME kinetics ,DIFFERENTIAL equations ,RUNGE-Kutta formulas - Abstract
In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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