Mathematical Modeling and Analysis of the Kinetics of Thermal Inactivation of Enzyme

Algorithm 1

Scilab/Matlab program to find the numerical solution of (2) and (3).

function main1

options= odeset (‘RelTol’,1e-6,‘Stats’,‘on’);

%initial conditions

T=100;

Xo = [1; 0; T+30];

tspan = [0,10];

tic

[t,X] = ode45(@TestFunction,tspan,Xo,options);

toc

figure

hold on

plot(t, X(:,1))

plot(t, X(:,2))

plot(t, X(:,3),‘.’)

legend(‘x1’,‘x2’,‘x3’)

ylabel(‘x’)

xlabel(‘t’)

return

function [dx_dt]= TestFunction(t,x)

k1=2;k2=0.1;k3=10^∧(-3);k4=2.66*10^∧(-3);K=4.44*10^∧(-2);T=100;

dx_dt(1) =-k1*x(1)+k2*x(2)^∧2-2*k3*x(1)^∧2;

dx_dt(2) =2*k1*x(1)-2*(k2+k4)*x(2)^∧2;

dx_dt(3)=K*(T-x(3));

dx_dt = dx_dt’;

return