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).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

See similar textbooks