enzymereactdiff.m

matlab在化学工程中的应用实例程序,对大家研究学习有指导作用。

function EnzymeReactDiff
% 氧扩散进入球形细胞中进行酶催化反应
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2003/06/29 $

clear all
clc
global epsilon k
a = 0;
b = 1;
epsilon = 0.1;
k = 0.1;

% solution is obtained using an initial guess of y1(x)=0, y2(x)=1 
solinit = bvpinit(linspace(a,b,50),[0 1]);
sol = bvp4c(@ODEfun,@BCfun,solinit);
x = [0:0.2:1];
y = deval(sol,x);
fprintf('Results:\n \tx\t\ty\n')
fprintf('\t%.4f  %.4f\n',[x; y(1,:)])

% 结果显示
x4plot = linspace(a,b,200);
y4plot = deval(sol,x4plot);
plot(x4plot,y4plot(1,:))
xlabel('x')
ylabel('y')

% ------------------------------------------------------------------
function dydx = ODEfun(x,y)
global epsilon k
fy1 = 1/epsilon * y(1)/(y(1)+k);
dydx(1) = y(2);
if x==0 
    dydx(2) = 0;
else
    dydx(2) = -2*y(2)/x + fy1;
end
dydx = dydx';

% ------------------------------------------------------------------
function bc = BCfun(ya,yb)
bc = [yb(1)-1; ya(2)];