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Numerical Methods: Runge-Kutta Formulas for Differential Equations

Learn Runge-Kutta methods up to order four for numerical solutions of differential equations. Understand the algorithm and implementation steps for accurate calculations.

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Numerical Methods: Runge-Kutta Formulas for Differential Equations

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  1. 1. Second order) RK method is K1  =  h f(xi, yi)K2  =  h f(xi + h/2, yi+ K1 /2)yi+1  =  yi+  (  K2 )                                             for i = 0, 1, 2 . . . or equivalently yi+1  =  yi+  h f(xi + h/2, yi+ h f(xi, yi)/2)       for i = 0, 1, 2 . . . 2. RK method of order three (v = 3) K1 = h f(xi, yi) K2 = h f(xi + h/2, yi + K1 /2) K3 = h f(xi + h, yi - K1 + 2K2 ) yi+1 = yi + ( K1 + 4K2 + K3 )/6 3. RK method of order four (v = 4) K1 = h f(xi, yi) K2 = h f(xi + h/2, yi + K1 /2) K3 = h f(xi + h/2, yi + K2 /2) K4 = h f(xi + h, yi + K3 ) yi+1 = yi + ( K1 + 2K2 + 2K3 + K4 )/6

  2. Hints !!!

  3. Assignment - 3 Q 1 Q 2 Q 3

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