Question

PLEASE PLEASE,ONLY ANSWER THIS QUESTION IF YOU COULD GIVE ME THE MATLAB CODE.THANK YOU.

Solve the following ODE from x = 4 to x = 4.5 using a step size of h = 0.5 with non-self-starting Heun Method, where y(3.5) = 0.244898 and y(4) = 0.1875. List the values for the Predictor and the Corrector with three iterations only. Make sure you include 4 decimals in your answer. dy dx 3y + = 0 Example answer: 0.2500 X DO) pl v (2) (3) 4.5

Answer 1

The answer is given by -

Page No. Date -34 dy da here, f (my) = -39 re and y (4) = 0.1875 y (3.5) - 0.244898 h = 0.5 tly we have to solve the given ODE from to =4.5 Predictor yiti - Yi+ h (f(Hiy:) yiti = y; +hf (2004;) + X; +, Xith =xito.5 2 ffrite situ)] |X, = 3.5 X2= 4 ×3=4.5 y = 0.1875 +0.5 ($14, 0-187) +44-3X0-1995) y=0.244898 2: 0.1875 43 = 0.1875+ OS -3x0-1875 + 3x 0176875 4 345 = 0.1875+1 -0.1171875 = 0.1875 + 1 [-0-140625 -6.078123 0.1328125 .34 Y: as dy dr X ay y = 0.1328125 for x 245. > c = 12. 1025 .. y = 12:1025 x3 y' - 12.1025 x 2 22 -- 605125 x2 i for x=4.5 - 0.2988 Now (2) ។ 6.05125 2 - for n=4.5 y 12) = 1.3447 Scanned with CamScanner

Paga Data Now, y (3) = 6.0512s. In (2) for n=4.5 (3) 6.05125 x 9.1017 15041 Hence, х yo) y" y (2) 0.1328125 -0.2988 1:3447 g.1017 Scanned with CamScanner