solution13

solution13 - % Assignment 13 % Prob. 1 fp1=inline('x.*y');

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% Prob. 1 fp1=inline('x.*y'); [x,y]=ode45(fp1,0:0.2:1,1); disp(' x y') disp(' ') disp([x,y]) x y 0 1 0.2 1.0202 0.4 1.0833 0.6 1.1972 0.8 1.3771 1.6487 % Prob 2 [t,theta]=ode45('fp2',0:0.2:1,[pi/4,0]); disp(' t theta') disp(' ') disp([t,theta(:,1)]) t theta 0.7854 0.56671 0.022259 -0.53541 -0.7842 -0.59618 % Prob 3 [t,y]=ode45('fp3',0:0.2:1.6,[1,1]); % The exact solution is yexact=cos(5*t)+sin(t); disp(' t y yexact') disp(' ') disp([t,y(:,1),yexact]) yexact 0.73894 0.73897 -0.026918 -0.026728 -0.42532 -0.42535 0.063922 0.063712 1.1255 1.1251 1.2 1.8922 1.4 1.7389 1.7394 1.6 0.85351 0.85407 % Prob 4 % Since the equations are non-linear, there are multiple solutions: each % depend on the initial guess. % 1st solution options=optimset('display','off'); Z1=fsolve('fp4',[1,1],options) % 2nd solution Z2=fsolve('fp4',[-1,-1],options) disp(' ') Z1 = 3 Z2 = -3 -1
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solution13 - % Assignment 13 % Prob. 1 fp1=inline('x.*y');

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