(adsbygoogle = window.adsbygoogle || []).push({}); 1. Solve y'=3t^2y^2 on [0, 3] , y0 = −1, using Euler method and Taylor method of

order 3. Compare your solutions to the exact solution. y(t)=(-1/((t^3)+1))

I DONT KNOW WHAT IS WRONG WITH MY PROGRAM! PLEASE HELP =D

2. Relevant equations

http://en.wikipedia.org/wiki/Euler_method

http://math.fullerton.edu/mathews/n2003/TaylorDEMod.html [Broken]

3. The attempt at a solution

function Euler2(a,b,h,y0)

t0=a;

t(1)=t0;

y(1)=y0;

N=(b-a)/h;

for i=1:N

y(i+1)=y(i)+h*(func(t(i),y(i)));

t(i+1)=t(i)+h;

end

-----------------------------------------

function deriv=func(t,y)

deriv=3*t^2*y^2;

-----------------------------------------

function w=Taylor1(a,b,h)

t0=a;

y0=1;

t(1)=t0;

y(1)=y0;

N=(b-a)/h;

w(1)=1;

%2nd Order Taylor Method%

for i=2:N+1

w(i)= w(i-1)+h*(1-h+(h^2)/2);

t(i)= a+i*h;

end

%3rd Order Taylor Method%

for i=2:N+1

w(i)= w(i-1)*(1-h+(h^2)/2-(h^3)/6);

t(i)= a+i*h;

end

------------------------------------------------

a=0;

b=3;

y0=-1;

h=0.1;

t=a:h:b;

w1=Euler2(a,b,h);

w2=Taylor2(a,b,h);

plot(t,w1,'r')

hold on

plot(t,w2,'b')

hold on

plot(t,-1/(t^3+1),'g')

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# Homework Help: Taylor and Euler Matlab Comparison for Numerical Analysis.

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