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function [c,f,s]=pdefun(x,t,u,dudx)
Pe_C=1;
Pe_T=1;
B_C=1;
B_T=2;
gamma=20;
beta_T=1;
u_c=0;
y=u(2)/(1+u(2)/gamma);
R_11=B_T*B_C*(1-u(1))*exp(y);
R_12=-beta_T*(u_c-u(2));
R_13=-B_C*(1-u(1))*exp(y);
c=[1 1]';
f=[1/Pe_C 1/Pe_T]'.*dudx;
s=[R_13-dudx(1) R_11+R_12-dudx(2)]';

function [pl,ql,pr,qr]=bcfun(xl,ul,xr,ur,t)
pl=[-ul(1),-ul(2)]';
ql=[1 1]';
pr=[0 0]';
qr=[1 1]';

function u0=icfun(x)
u0=[0 0]';
m=0;
t=linspace(0,1,500);
x=linspace(0,1,100);
sol=pdepe(m,@pdefun,@icfun,@bcfun,x,t);
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