Unformatted text preview: 1) / . 005 = 200 steps to approximate the solution on [1 , 2]. With the initial input x = x = 1, y = y = − . 414, we get k 1 = hf ( x, y ) = 0 . 005[2(1) − 4 − ( − . 414) 2 ] = 0 . 009143; k 2 = hf ( x + h/ 2 , y + k 1 / 2) = 0 . 005[2(1 + 0 . 005 / 2) − 4 − ( − . 414 + 0 . 009143 / 2) 2 ] = 0 . 009062; k 3 = hf ( x + h/ 2 , y + k 2 / 2) = 0 . 005[2(1 + 0 . 005 / 2) − 4 − ( − . 414 + 0 . 009062 / 2) 2 ] = 0 . 009062; k 4 = hf ( x + h, y + k 3 ) = 0 . 005[2(1 + 0 . 005) − 4 − ( − . 414 + 0 . 009062) 2 ] = 0 . 008983; ⇓ x = 1 + 0 . 005 = 1 . 005 , y = − . 414 + 1 6 (0 . 009143 + 2 · . 009062 + 2 · . 009062 + 0 . 008983) ≈ − . 404937; . . . 158...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Approximation, decimal places, RungeKutta subroutine approximations, order RungeKutta, following Table 3I

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