Runge Kutta Methods Runge Kutta Methods Runge Kutta

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Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods 1. Second order) RK method is K 1 = h

Runge - Kutta Methods 1. Second order) RK method is K 1 = h f(xi, yi) K 2 = h f(xi + h/2, yi + K 1 /2 ) yi+1 = yi + ( K 2 ) 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) K 1 = h f(xi, yi) K 2 = h f(xi + h/2, yi + K 1 /2) K 3 = h f(xi + h, yi - K 1 + 2 K 2 ) y = yi + ( K 1 + 4 K 2 + K 3 )/6 i+1 3. RK method of order four (v = 4) K 1 = h f(xi, yi) K 2 = h f(xi + h/2, yi + K 1 /2) K 3 = h f(xi + h/2, yi + K 2 /2) K 4 = h f(xi + h, yi + K 3 ) yi+1 = yi + ( K 1 + 2 K 2 + 2 K 3 + K 4 )/6

Runge - Kutta Methods • Hints !!!

Runge - Kutta Methods • Hints !!!

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Runge - Kutta Methods

Q 1 Q 2 Q 3 Assignment - 3

Q 1 Q 2 Q 3 Assignment - 3

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