MATLAB Program for Taylor's Method of Order 2
% Taylor's method of order 2
% Example 1: Approximate the solution to the initial-value
problem
% dy/dt=e^t ; 0<=t<=2
; y(0)=1;
% Example 2: Approximate the solution to the initial-value
problem
% dy/dt=y-t^2+1 ;
0<=t<=2 ; y(0)=0.5;
%f = @(t,y) (0*y+exp(t));
%fprime = @(t,y)
(0*y+exp(t)); % f=e^t, f'=e^t
f = @(t,y)
(y-t^2+1);
fprime=@(t,y) (y-t^2+1-2*t); % y'=f=y-t^2+1, f'=y'-2t+0
=y-t^2+1-2t
a = input('Enter left end ponit, a: ');
b = input('Enter right end point, b: ');
n = input('Enter no. of subintervals, n:
');
alpha =
input('Enter
the initial condition, alpha: ');
h =
(b-a)/n;
t=[a
zeros(1,n)];
w=[alpha
zeros(1,n)];
for i = 1:n+1
t(i+1)=t(i)+h;
wprime=f(t(i),w(i))+(h/2)*fprime(t(i),w(i));
w(i+1)=w(i)+h*wprime;
fprintf('%5.4f %11.8f\n', t(i), w(i));
plot(t(i),w(i),'r*'); grid on;
xlabel('t values'); ylabel('w values');
hold on;
end
>> TaylorMethodofOrder2
Enter left end ponit, a: 0
Enter right end point, b: 2
Enter no. of subintervals, n: 10
Enter the initial condition, alpha: 1
0.0000 1.00000000
0.2000 1.44000000
0.4000 1.96000000
0.6000 2.56000000
0.8000 3.24000000
1.0000 4.00000000
1.2000 4.84000000
1.4000 5.76000000
1.6000 6.76000000
1.8000 7.84000000
2.0000 9.00000000
>>
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