Use 4-step Adams-Bashforth method with h = 0:1 to approximate the solution of th

Question

Use 4-step Adams-Bashforth method with h = 0:1 to approximate the solution of the following
initial-value problem:
y' = -5y + 5t^2 + 2t with 0 < t < 1 and y(0) =1/3

Use Runge-Kutta method of order four to obtain starting values. Compare the results with the actual
solution y(t) = t^2 + 1/3 e^(-5*t)

Explanation / Answer

% save as adamb2.m %% forth order predator-corrector method Method for ODE % y'(x) = -5y + 5t^2 + 2t ; t>0, % y(0) = 1/3 >0 % %% %clear all f = @ (t , y) (-5*y + 5*t^2 + 2*t ); h=0.1 ; tmax = 1 ; n= tmax/h ; t(1)= 0 ; y(1)= 1/3 ; tout=t(1) ; yout=y(1).'; true(1)=1/3 ; ero(1)=0 ; disp(' t numerical exact error ') disp('~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~') for i=1:(n+1) t(i+1) = i*h ; if i> adamb2 t numerical exact error ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.00 0.3333333 0.3333333 0.0000000 0.10 0.2122830 0.2121769 0.0001061 0.20 0.1627655 0.1626265 0.0001390 0.30 0.1645165 0.1643767 0.0001398 0.40 0.2048557 0.2051118 0.0002561 0.50 0.2769896 0.2773617 0.0003721 0.60 0.3762804 0.3765957 0.0003153 0.70 0.4998012 0.5000658 0.0002646 0.80 0.6458949 0.6461052 0.0002103 0.90 0.8135498 0.8137030 0.0001532 1.00 1.0021372 1.0022460 0.0001088

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