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part c
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nin13001
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Dec 6, 2017
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,22 @@ | ||
| function y=Prob2ptC(ode,dt,y0,tlimits) | ||
| maxit=100; | ||
| t=[tlimits(1):dt:tlimits(2)]; | ||
| y=zeros(length(t),1); | ||
| y(1)=y0; | ||
| for i=2:length(t) | ||
| dy=ode(t(i-1),y(i-1)); | ||
| y(i)=y(i-1)+dt*dy; | ||
| dyc=(dy+ode(t(i),y(i)))/2; | ||
| y(i)=y(i-1)+dt*dyc; | ||
| nits=1; | ||
|
|
||
| while(1) | ||
| nits=nits+1; | ||
| yold=y(i); | ||
| dyc=(dy+ode(t(i),y(i)))/2; | ||
| y(i)=y(i-1)+dt*dyc; | ||
| ea=abs(yold-y(i))/y(i)*100; | ||
| if ea<.0001|nits>maxit;break;end; | ||
| end; | ||
| end | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,22 @@ | ||
| function y=Prob2ptC(ode,dt,y0,tlimits) | ||
| maxit=100; | ||
| t=[tlimits(1):dt:tlimits(2)]; | ||
| y=zeros(length(t),1); | ||
| y(1)=y0; | ||
| for i=2:length(t) | ||
| dy=ode(t(i-1),y(i-1)); | ||
| y(i)=y(i-1)+dt*dy; | ||
| dyc=(dy+ode(t(i),y(i)))/2; | ||
| y(i)=y(i-1)+dt*dyc; | ||
| nits=1; | ||
|
|
||
| while(1) | ||
| nits=nits+1; | ||
| yold=y(i); | ||
| dyc=(dy+ode(t(i),y(i)))/2; | ||
| y(i)=y(i-1)+dt*dyc; | ||
| ea=abs(yold-y(i))/y(i)*100; | ||
| if ea<.0001|nits>maxit;break;end; | ||
| end; | ||
| end | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,17 @@ | ||
| set(0, 'defaultAxesFontSize', 16) | ||
| set(0,'defaultTextFontSize',14) | ||
| set(0,'defaultLineLineWidth',3) | ||
| dt = 0.1; | ||
| t = [0:dt:3]; | ||
| y = zeros(size(t)); | ||
| y(1) = 1; | ||
| for i = 2:length(t) | ||
| dy = prob2_ode(t,y(i-1)); | ||
| y(i) = y(i-1)+dt*dy; | ||
| end | ||
| a = figure(1); | ||
| y_heun = Prob2ptC (@(t,y) prob2_ode(t,y), 0.1, 1, [0 3]); | ||
| plot(t,exp(-t),'k-',t,y,'Xg',t,y_heun,'Or'); | ||
| legend('Analytical','Euler','Heun','Location','Northeast') | ||
| xlabel('Time') | ||
| ylabel('Position') |