lect_15 - Numerical Marine Hydrodynamics Numerical...

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Numerical Marine Hydrodynamics Numerical Differentiation – Newton Interpolation – Finite Differences Ordinary Differential Equations – Initial Value Problems • Euler’s Method • Taylor Series Methods – Error analysis • Predictor-Corrector Methods • Runge-Kutta Methods • Stiff Differential Equations • Multistep Methods – Systems of differential equations – Boundary Value Problems • Shooting method • Direct Finite Difference methods Numerical Marine Hydrodynamics Lecture 15 2.29
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Ordinary Differential Equations Initial Value Problems Euler’s Method Differential Equation Example Discretization Finite Difference (forward) Recurrence euler.m Numerical Marine Hydrodynamics Lecture 15 2.29
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Lecture 15 Numerical Marine Hydrodynamics 2.29 Initial Value Problems Predictor-Corrector methods Heun’s Method Initial Slope Estimate Predictor Corrector Endpoint Derivative Estimate Average Derivative Estimate x i x i+1 x i x i+1 Iterative Heun k k+1
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Predictor-Corrector methods Midpoint Method Midpoint Estimate x i x i+1 x i x i+1 x i+1/2 Midpoint Derivative Estimate Midpoint Recurrence Heun’s and Midpoint methods are superior to Euler’s method as they use an intermediate estimate of the derivative. Numerical Marine Hydrodynamics
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.29 taught by Professor Henrikschmidt during the Spring '07 term at MIT.

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lect_15 - Numerical Marine Hydrodynamics Numerical...

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