I need your help. y'(t) = -30*y+30*t^2+2*t; y(0)=1, & exact solution is y(t)=e^-30*x +x^2. i can't understand what is different b/w kr4 plotting & its error . i need both graph n error please send me code.

function rungekutta123
h = 0.05;
t = 0;
w = 1;
fprintf('Step 0: t = %12.8f, w = %12.8f\n', t, w);
for i=1:50
k1 = h*f(t,w);
k2 = h*f(t+h/2, w+k1/2);
k3 = h*f(t+h/2, w+k2/2);
k4 = h*f(t+h, w+k3);
w = w + (k1+2*k2+2*k3+k4)/6;
t = t + h;
fprintf('Step %d: t = %6.4f, w = %18.15f\n', i, t, w);
end
%%%%%%%%%%%%%%%%%%
function v = f(t,y)
v = -30*y+30*t^2+2*t;

[jamila nizamani]

sorry Exact solution is y(t)=e^-30*t + t^2.

[Image Analyst]

Please read this: http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup and fix your formatting.

Answer 1

[Mischa Kim]

Are you trying to plot the result? If so, just save the integration step results in a matrix:

function rungekutta123
h = 0.05;
t = 0:0.05:2.5;
w(1) = 1;
fprintf('Step 0: t = %12.8f, w = %12.8f\n', t, w);
for ii=1:(length(t)-1)
    k1 = h*f(t(ii),w(ii));
    k2 = h*f(t(ii)+h/2, w(ii)+k1/2);
    k3 = h*f(t(ii)+h/2, w(ii)+k2/2);
    k4 = h*f(t(ii)+h,   w(ii)+k3);
    w(ii+1) = w(ii) + (k1+2*k2+2*k3+k4)/6;

    fprintf('Step %d: t = %6.4f, w = %18.15f\n', ii, t(ii), w(ii));
end

y_exact = exp(-30.*t) + t.^2;
subplot(2,1,1)
plot(t,w,t,y_exact)
ylabel('Exact vs. approximated function')

subplot(2,1,2)
plot(t,w - y_exact)
ylabel('Error')

%%%%%%%%%%%%%%%%%%
function v = f(t,y)
v = -30*y+30*t^2+2*t;

[jamila nizamani]

Step 0: t = 0.00000000, w = 0.05000000 Step 0: t = 0.10000000, w = 0.15000000 Step 0: t = 0.20000000, w = 0.25000000 Step 0: t = 0.30000000, w = 0.35000000 Step 0: t = 0.40000000, w = 0.45000000 Step 0: t = 0.50000000, w = 0.55000000 Step 0: t = 0.60000000, w = 0.65000000 Step 0: t = 0.70000000, w = 0.75000000 Step 0: t = 0.80000000, w = 0.85000000 Step 0: t = 0.90000000, w = 0.95000000 Step 0: t = 1.00000000, w = 1.05000000 Step 0: t = 1.10000000, w = 1.15000000 Step 0: t = 1.20000000, w = 1.25000000 Step 0: t = 1.30000000, w = 1.35000000 Step 0: t = 1.40000000, w = 1.45000000 Step 0: t = 1.50000000, w = 1.55000000 Step 0: t = 1.60000000, w = 1.65000000 Step 0: t = 1.70000000, w = 1.75000000 Step 0: t = 1.80000000, w = 1.85000000 Step 0: t = 1.90000000, w = 1.95000000 Step 0: t = 2.00000000, w = 2.05000000 Step 0: t = 2.10000000, w = 2.15000000 Step 0: t = 2.20000000, w = 2.25000000 Step 0: t = 2.30000000, w = 2.35000000 Step 0: t = 2.40000000, w = 2.45000000 Step 0: t = 2.50000000, w = 1.00000000 ??? Undefined function or method 'f' for input arguments of type 'double'.

Error in ==> rungekutta1234 at 7 k1 = h*f(t(ii),w(ii)); thank you so much but, this is my answer and graph is not plot, error is also there please help me

[jamila nizamani]

sir i need a graph and [wrk4-wexact] error i means w_true, i hope you understand my problem.

[Mischa Kim]

I only showed the part of the code that needed changing. Should now be complete, see above.

[jamila nizamani]

Mischa kim, thank you so much for all of your help!

Answer 2

[Nurcan]

y(t)=f(t, y(t)) y(t0)=y0 tE[t0, T] f(t,y)=-y/(2*t)+t^2 t0=1 T=2 y0=1