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Question (3) Write only one step of the 2nd order Runge-Kutta method in solving the following differential equation. Only find Y(0.08) and Z(0.08). Y(0)= 25 d'Y -+(r'-x)4 dY +5Y 0 dx dY h = Ax = 0.08 (0)%3 38 dx dx? 2nd order Runge- Kutta Method: Skin = h f(x, , S,) k,, =h f(x, +h, S, +. 1 Xp41 = x, +h , S = S, +(k, +k2,) n+1 In ("y+ "s dY Z Y Definitions: S = ds dx = f(x , S)= dx dz r-y2 5Y dx

Question (3) Write only one step of the 2nd order Runge-Kutta method in solving the following differential equation. Only find Y(0.08) and Z(0.08). Y(0)= 25 d'Y -+(r'-x)4 dY +5Y 0 dx dY h = Ax = 0.08 (0)%3 38 dx dx? 2nd order Runge- Kutta Method: Skin = h f(x, , S,) k,, =h f(x, +h, S, +. 1 Xp41 = x, +h , S = S, +(k, +k2,) n+1 In ("y+ "s dY Z Y Definitions: S = ds dx = f(x , S)= dx dz r-y2 5Y dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question (3) Write only one step of the 2nd order Runge-Kutta method in solving the following differential equation. Only find Y(0.08) and Z(0.08). Y(0)= 25 d?Y dY +(Y² -x)+5Y = 0 dx dy h = Ax = 0.08 dx 2nd order Runge - Kutta Method: Skin = h f(x, , S,) ("y+ "x);+ "s = "s |k2n = h f(x, +h , S, +k,) 1 Xp+1 = x, +h n+1 2 dY Y Definitions: S = Z s=. -(x, s) = dx dZ X-Y2 -5Y dx
Transcribed Image Text:Question (3) Write only one step of the 2nd order Runge-Kutta method in solving the following differential equation. Only find Y(0.08) and Z(0.08). Y(0)= 25 d?Y dY +(Y² -x)+5Y = 0 dx dy h = Ax = 0.08 dx 2nd order Runge - Kutta Method: Skin = h f(x, , S,) ("y+ "x);+ "s = "s |k2n = h f(x, +h , S, +k,) 1 Xp+1 = x, +h n+1 2 dY Y Definitions: S = Z s=. -(x, s) = dx dZ X-Y2 -5Y dx
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