A study of nonlinear biochemical reaction model

2016 ◽  
Vol 09 (05) ◽  
pp. 1650071 ◽  
Author(s):  
Muhammad Asad Iqbal ◽  
Syed Tauseef Mohyud-Din ◽  
Bandar Bin-Mohsin
Keyword(s):  
Differential Equations ◽  
Reaction Model ◽  
Numerical Results ◽  
Picard Iteration ◽  
System Of Differential Equations ◽  
Legendre Wavelets ◽  
Enzyme Substrate ◽  
Runge Kutta Method ◽  
Picard Method ◽  
Order Four

The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method (LWPM). Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge–Kutta method of order four (RK-4). Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.

scholarly journals Flow of a Jeffrey Fluid Between Two Long Vertical Thin Plates with Porous Medium

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1059
Author(s):  
S. Sreenadh ◽  
B. Govindarajulu ◽  
A. N.S. Srinivas ◽  
R. Nageshwar Rao
Keyword(s):  
Porous Medium ◽  
Temperature Distribution ◽  
Fluid Velocity ◽  
Numerical Results ◽  
Thin Plates ◽  
Jeffrey Fluid ◽  
Runge Kutta Method ◽  
Fluid Parameter ◽  
Permeability Parameter ◽  
Order Four

The present study investigates fully developed free - convection Jeffrey fluid flow between two vertical plates with porous medium. The vertical plates are moving with same velocity but in opposite directions. The coupled nonlinear governing equations are solved by using the linearization technique. The solutions for velocity distribution, temperature distribution, skin friction and rate of heat transfer is obtained in the presence of porous medium by Iterative procedure.  Shooting technique with Runge - Kutta method of order four is proposed to compare the numerical results for velocity and temperature distribution. The numerical results obtained by both methods are compared and presented graphically. It is observed that an increase in the permeability parameter causes decrease in the fluid velocity and an increase in the Jeffrey fluid parameter causes an enhancement in the fluid velocity. The significance of various pertinent parameters like Grashof number, Prandtl number, Eckert number and the plate velocity are explained through graphs.  

PERIODIC ORBITS IN THE NEWTON–LEIPNIK SYSTEM

2002 ◽  
Vol 12 (03) ◽  
pp. 511-523 ◽  
Author(s):  
BENJAMIN A. MARLIN
Keyword(s):  
Periodic Solution ◽  
Nonlinear System ◽  
Differential Equations ◽  
Periodic Orbits ◽  
Closed Orbit ◽  
Numerical Results ◽  
Asymptotically Stable ◽  
System Of Differential Equations ◽  
Promising Candidate ◽  
Closed Orbits

This paper considers an autonomous nonlinear system of differential equations derived in [Leipnik, 1979]. A criterion for the existence of closed orbits in similar systems is presented. Numerical results are made rigorous by the use of interval analytic techniques in establishing the existence of a periodic solution which is not asymptotically stable. The limitations of the method of locating orbits are considered when a promising candidate for a closed orbit is shown not to intersect itself.

scholarly journals A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

2020 ◽  
Vol 17 (1) ◽  
pp. 0166
Author(s):  
Hussain Et al.
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

scholarly journals Analytical solution of system of differential equations by variational iteration method

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 77-86
Author(s):  
Jamshad Ahmed ◽  
Faizan Hussain
Keyword(s):  
Linear System ◽  
Analytical Solution ◽  
Differential Equations ◽  
Iteration Method ◽  
Graphical Representation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Results ◽  
System Of Differential Equations ◽  
Non Linear System

In this paper, Varitational Iteration Method using He’s Polynomials is used to construct the exact as well as approximate solutions of differential equations. From the obtained numerical results, it has been observed that this proposed technique is very efficient and reliable for the solution of the linear and non-linear system of differential equations. Numerical results and graphical representation reflect the accuracy and effectiveness of the proposed modification.BIBECHANA 13 (2016) 77-86

scholarly journals Application of Differential Transformation Method for Solving HIV Model with Anti-Viral Treatment

2020 ◽  
Vol 14 (3) ◽  
pp. 378-388
Author(s):  
Esther Y. Bunga ◽  
Meksianis Z. Ndii
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Time Step ◽  
Differential Transformation ◽  
Runge Kutta Method ◽  
Runge Kutta

Mathematical models have been widely used to understand complex phenomena. Generally, the model is in the form of system of differential equations. However, when the model becomes complex, analytical solutions are not easily found and hence a numerical approach has been used. A number of numerical schemes such as Euler, Runge-Kutta, and Finite Difference Scheme are generally used. There are also alternative numerical methods that can be used to solve system of differential equations such as the nonstandard finite difference scheme (NSFDS), the Adomian decomposition method (ADM), Variation iteration method (VIM), and the differential transformation method (DTM). In this paper, we apply the differential transformation method (DTM)  to solve system of differential equations. The DTM is semi-analytical numerical technique to solve the system of differential equations and provides an iterative procedure to obtain the power series of the solution in terms of initial value parameters.. In this paper, we present a mathematical model of HIV with antiviral treatment and construct a numerical scheme based on the differential transformation method (DTM) for solving the model. The results are compared to that of Runge-Kutta method. We find a good agreement of the DTM and the Runge-Kutta method for smaller time step but it fails in the large time step.

Some analytical and numerical solutions for the safe turn manoeuvres of agricultural aircraft – an overview

2007 ◽  
Vol 111 (1123) ◽  
pp. 593-599 ◽  
Author(s):  
B. Rasuo
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Numerical Results ◽  
System Of Differential Equations ◽  
Bank Angle ◽  
Tangential Load ◽  
Load Factors ◽  
The Mathematical Model

Abstract In this paper, a theoretical study of the turn manoeuvre of an agricultural aircraft is presented. The manoeuvre with changeable altitude is analyzed, together with the, effect of the load factors on the turn manoeuvre characteristics during the field-treating flights. The mathematical model used describes the procedure for the correct climb and descent turn manoeuvre. For a typical agricultural aircraft, the numerical results and limitations of the climb, horizontal and descending turn manoeuvre are given. The problem of turning flight with changeable altitude is described by the system of differential equations which describe the influence of the normal and tangential load factors on velocity, the path angle in the vertical plane and the rate of turn, as a function of the bank angle during turning flight. The system of differential equations of motion was solved on a personal computer with the Runge-Kutta-Merson numerical method. Some analytical and numerical results of this calculation are presented in this paper.

Numerical Solution of Volterra Integro-Differential Equations Using Improved Runge-Kutta Methods

2019 ◽  
Vol 892 ◽  
pp. 193-199
Author(s):  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Nafsiah Md Lazim ◽  
Fudziah Ismail ◽  
Zanariah Abdul Majid
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Quadrature Rule ◽  
Numerical Results ◽  
Test Problems ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Interpolation Polynomials

In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the integral operator in Volterra integro-differential equation is approximated using quadrature rule and Lagrange interpolation polynomials. To illustrate the efficiency of proposed methods, the test problems are carried out and the numerical results are compared with existing third and fourth order classical Runge-Kutta method with 3 and 4 stages, respectively. The numerical results showed that the Improved Runge-Kutta method by achieving the higher accuracy performed better results than existing methods.

Flow in Straight Ducts of Arbitrary Cross Section

1979 ◽  
Vol 46 (2) ◽  
pp. 263-268 ◽  
Author(s):  
P. W. Duck
Keyword(s):  
Fourier Series ◽  
Conformal Mapping ◽  
Differential Equations ◽  
Cross Section ◽  
Coupled System ◽  
Arbitrary Cross Section ◽  
Numerical Results ◽  
Steady Flows ◽  
System Of Differential Equations ◽  
Oscillatory Flows

A method is presented for treating flows in straight ducts. The method involves the conformal mapping of the cross section on to a semicircle, and then solving the problem using Fourier series. For oscillatory flows (to which most of the paper is devoted) the method results in an infinite, coupled system of differential equations, although reliable numerical results may be obtained by truncation. For steady flows, however, the method yields a solution involving integrals of the Jacobian of the transformation.

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