Lec06_ME262_SolutionOfODE.ppt - ME 262 Numerical Analysis Sessional Department of Mechanical Engineering BUET Runge-Kutta method to solve first order

Lec06_ME262_SolutionOfODE.ppt - ME 262 Numerical Analysis...

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ME 262: Numerical Analysis Sessional Department of Mechanical Engineering, BUET Department of Mechanical Engineering, BUET
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Runge-Kutta method to solve first order differential equations June 25, 2020 ME262 Numerical Analysis Sessional 2 The Euler Method y i+1 = y i + h f(x i , y i ) There are several reasons that Euler’s method is not recommended for practical use, among them, (i) the method is not very accurate when compared to others, and (ii) neither is it very stable.
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June 25, 2020 ME262 Numerical Analysis Sessional 3 Runge-Kutta method to solve first order differential equations Fourth-order Runge Kutta y i+1 = y i + (1/6) (k1 +2 k2 +2 k3 + k4) where k1 = h*f(x i , y i ) k2 = h*f(x i + h/2, y i + k1/2) k3 = h*f(x i + h/2, y i + k2/2) k4 = h*f(x i + h, y i + k3)
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June 25, 2020 ME262 Numerical Analysis Sessional
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  • K1, Runge–Kutta methods, Numerical ordinary differential equations, Numerical Analysis Sessional

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