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# 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
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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Initial Value Problems 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.
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lect_15 - Numerical Marine Hydrodynamics Numerical...

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