Two ODEs are:
F"=G(G^2+gamma^2)/(G^2+lambda*gamma^2)
G'= 1/3F'^2-2/3(F*F")
subject to: F(xi)=alpha/2, F'(xi)=1 at xi=0 where 'alpha' is a parameter (wall parameter)
F'(xi)= 0 as xi tends to infinity
I should be getting a multiple graphs varying the parameter ' alpha'
The code that I have run is:
function sol= projclc;clf;clear;global lambda gama alplambda=0.5;gama=1;pp=[0:0.5:1.0];figure(1)plot(2,1);solinit= bvpinit([0:0.01:10],[0,1,0]);for alp= ppsol= bvp4c(@projfun,@projbc,solinit);solinit= sol;plot(2,1);plot(sol.x,sol.y(2,:))endendfunction f= projfun(x,y)global lambda gamaf= [y(2);y(3)*(y(3)^2+gama.^2)/(y(3)^2+lambda*gama.^2);y(2)^2/3-(2*y(1)*y(3)*(y(3)^2+gama.^2))/(3*(y(3)^2+lambda*gama.^2))];endfunction res= projbc(ya,yb)global alpres= [ya(1)-alp/2; ya(2)-1.0; yb(2)];end
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