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2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: Solve for k, and k,. k = hf(xn, Yn) k2 = hf(xn + h,yn + k1) and then, solve for the next value of y: Yn+1 = Yn +; (k1 + k2) for n = 1,2,... Уп+1 where x, = x, + nh. Now, try to solve the initial value problem y' = xy/(x +y)' y' = xy/(x² + y2 with y(1) = 1 and h 0.2 over the interval 1s xs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth- order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order).

2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: Solve for k, and k,. k = hf(xn, Yn) k2 = hf(xn + h,yn + k1) and then, solve for the next value of y: Yn+1 = Yn +; (k1 + k2) for n = 1,2,... Уп+1 where x, = x, + nh. Now, try to solve the initial value problem y' = xy/(x +y)' y' = xy/(x² + y2 with y(1) = 1 and h 0.2 over the interval 1s xs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth- order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order).

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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2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: Solve for k, and k,. k1 = hf(xn,Yn) k2 = hf(xn + h,yn + k1) and then, solve for the next value of y: Yn+1 = Yn +(k1 + k2) for n = 1, 2,... where x, = x, + nh. Now, try to solve the initial value problem y' = xy/(x² + y/2 with y(1) = 1 and h = 0.2 over the interval 1s Xs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth- order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order).
Transcribed Image Text:2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: Solve for k, and k,. k1 = hf(xn,Yn) k2 = hf(xn + h,yn + k1) and then, solve for the next value of y: Yn+1 = Yn +(k1 + k2) for n = 1, 2,... where x, = x, + nh. Now, try to solve the initial value problem y' = xy/(x² + y/2 with y(1) = 1 and h = 0.2 over the interval 1s Xs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth- order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order).
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