function ch3ex8 sol = bvpinit(linspace(0,1,5),[1 1 1 1]); n = 5e-2; lambda = 2; fprintf(' kappa computed Os approximate Os \n') for kappa = 2:5 eta = lambda^2/(n*kappa^2); sol = bvp4c(@odes,@bcs,sol,[],n,lambda,eta); K2 = lambda*sinh(kappa/lambda)/(kappa*cosh(kappa)); approx = 1/(1 - K2); computed = 1/sol.y(3,end); fprintf(' %2i %10.3f %10.3f \n',kappa,computed,approx); end % v and C are computed separately on 0 <= x <= 1 and 1 <= x <= lambda. % A change of independent variable is used for the second interval. % First it must be undone to obtain the corresponding mesh in x and % then a solution assembled for all of 0 <= x <= lambda. x = [sol.x sol.x*(lambda-1)+1]; y = [sol.y(1:2,:) sol.y(3:4,:)]; plot(x,y(1,:),x,y(2,:)) legend('v(x)','C(x)') %print -depsc ch3fig8 %================================================= function dydx = odes(x,y,n,lambda,eta) dydx = [ (y(2) - 1)/n (y(1)*y(2) - x)/eta (lambda - 1)*(y(4) - 1)/n (lambda - 1)*(y(3)*y(4) - 1)/eta ]; function res = bcs(ya,yb,n,lambda,eta) res = [ ya(1); yb(4)-1; yb(1)-ya(3); yb(2)-ya(4)];