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andyreagan/gist:7905737

Last active December 31, 2015 00:09
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just took the derivative of rk4 by hand...
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gistfile1.matlab
L = L*(eye(dim) + h/6*(feval(J,t,y,params)+2*feval(J,t+h/2,y+h/2*s1,params)*(eye(dim)+h/2*feval(J,t,y,params))+2*feval(J,t+h/2,y+h/2*s2,params)*(eye(dim)+h/2*feval(J,t+h/2,y+h/2*s1,params))*(eye(dim)+h/2*feval(J,t,y,params))+feval(J,t+h,y+h*s3,params)*(eye(dim)+h*feval(J,t+h/2,y+h/2*s2,params))*(eye(dim)+h/2*feval(J,t+h/2,y+h/2*s1,params))*(eye(dim)+h/2*feval(J,t,y,params))));
%% BETTER
L1 = feval(J,t,y,params);
L2 = feval(J,t+h/2,y+h/2*s1,params)*(eye(dim)+h/2*L1);
L3 = feval(J,t+h/2,y+h/2*s2,params)*(eye(dim)+h/2*L2);
L4 = feval(J,t+h,y+h*s3,params)*(eye(dim)+h*L3);
L = L*(eye(dim) + h/6*(L1 + 2*L2 + 2*L3 + L4));
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