Solution method for the transformed time-dependent Michaelis–Menten enzymatic reaction model

Li, Ronald; Gorder, Robert A. Van; Mallory, Kristina; Vajravelu, K.

doi:10.1007/s10910-014-0397-y

Cited by 5 publications

(5 citation statements)

References 43 publications

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“…In 1992, Liao proposed HAM to serve as a general analytical method for solving nonlinear problems [32]. The accuracy and robustness of the HAM for solving nonlinear boundary value problems has been repeatedly confirmed in a wide range of papers, including: Lane-Emden equation [33], time-dependent Michaelis-Menton equation [34], non-local Whitham equation [35], and Zakharov system [36] to name a few. Here we outline the solution method and later discuss the convergence and accuracy of the HAM solution.…”

Section: Analytic Solution Via Homotopy Analysis Methodsmentioning

confidence: 99%

Effects of second-order slip and drag reduction in boundary layer flows

Vajravelu

Dewasurendra

et al. 2018

Applied Mathematics and Nonlinear Sciences

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In this paper, boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is analyzed. The governing partial differential equations are converted in to a nonlinear ordinary differential equation through an appropriate similarity transformation. The resulting nonlinear equation is solved via homotopy analysis method (HAM). Errors ranging from 10–7 to 10–10 are reported for a relatively few terms. The effects of the pertinent parameters on the velocity and the shear stress are presented graphically and discussed. In the absence of magnetic field and the two slip parameters, the results are found to be in excellent agreement with the available results in the literature. It is expected that the results obtained will not only provide useful information for industrial applications but also complement the earlier works.

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Section: Analytic Solution Via Homotopy Analysis Methodsmentioning

confidence: 99%

Effects of second-order slip and drag reduction in boundary layer flows

Vajravelu

Dewasurendra

et al. 2018

Applied Mathematics and Nonlinear Sciences

Self Cite

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“…Furthermore, analytical approaches permitting the control of error, such as the optimal homotopy analysis method, rely on assigning an error control parameter to each state variable. Reduction of dimension can allow one to minimize error via a single control parameter [2], rather than over multiple parameters [79], which is computationally less demanding.…”

Section: Discussionmentioning

confidence: 99%

“…In the present paper, we shall consider reduction of dimension for nonlinear dynamical systems. This approach has previously been employed in the literature in order to enable the construction of Lyapunov functions [1] and equilibrium dynamics [2], as well as to allow one to more easily approximate chaotic attractors analytically [3,4,5,6]. One method for reduction of dimension is differential elimination, in which one algorithmically reduces the nonlinear dynamical system into a single ordinary differential equation (ODE) for one of the state variables.…”

Section: Introductionmentioning

confidence: 99%

“…This approach has been applied when using Taylor series, approximate Fourier series, and asymptotic expansions in other types of basis functions to the solution of a system of nonlinear ODE. In hybrid analytic-numeric methods, such as the homotopy analysis method [7,8,9], such reductions of a system to a single equation also simplifies the optimization problem which is solved to obtain the error-minimizing solution (see, for instance, [2], where the present approach is used in such a capacity). Therefore, the reduction of order can greatly reduce the complexity of analytical calculations under several frameworks.…”

Section: Introductionmentioning

confidence: 99%

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Reduction of dimension for nonlinear dynamical systems

Harrington

Gorder

2016

Nonlinear Dyn

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We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where this reduction is possible, we employ differential elimination to obtain the reduced system. While analytical, the approach is algorithmic and is implemented in symbolic software such as MAPLE or SageMath. In other cases, the reduction cannot be performed strictly in terms of differential operators, and one obtains integro-differential operators, which may still be useful. In either case, one can use the reduced equation to both approximate solutions for the state variables and perform chaos diagnostics more efficiently than could be done for the original higherdimensional system, as well as to construct Lyapunov functions which help in the large-time study of the state variables. A number of chaotic and hyperchaotic dynamical systems are used as examples in order to motivate the approach.

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“…In addition, he found that when the progress curves are analyzed by the direct solution of the integrated Michaelis-Menten equation, there were three different demonstrated approximations of W(x) with relatively high accuracy that are appropriate to utilize. In many studies, they studied this system and proposed many different kinds of approximate analytical solutions [5][6][7][8][9]. Hussam et al [10] investigated the semianalytical results of fractional time enzyme kinetics using the Laplace transformation and Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

Alqhtani

Saad

2021

Fractal Fract

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In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.

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Solution method for the transformed time-dependent Michaelis–Menten enzymatic reaction model

Cited by 5 publications

References 43 publications

Effects of second-order slip and drag reduction in boundary layer flows

Effects of second-order slip and drag reduction in boundary layer flows

Reduction of dimension for nonlinear dynamical systems

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

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