lecture41 - CMPSC/MATH 451 Numerical Computations Lecture...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 41 Dec 7, 2011 Prof. Kamesh Madduri Class Overview Runge-Kutta methods Slides from textbook follow. 2 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Single-Step Methods Extrapolation Methods Multistep Methods Numerical Methods for ODEs There are many different methods for solving ODEs, most of which are of one of following types Taylor series Runge-Kutta Extrapolation Multistep Multivalue We briefly consider each of these types of methods Michael T. Heath Scientific Computing 61 / 84 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Single-Step Methods Extrapolation Methods Multistep Methods Taylor Series Methods Eulers method can be derived from Taylor series expansion By retaining more terms in Taylor series, we can generate higher-order single-step methods For example, retaining one additional term in Taylor series y ( t + h ) = y ( t ) + h y ( t ) + h 2 2 y 00 ( t ) + h 3 6 y 000 ( t ) + gives second-order method y k +1 = y k + h k y k + h 2 k 2 y 00 k Michael T. Heath Scientific Computing 62 / 84 Ordinary Differential Equations...
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lecture41 - CMPSC/MATH 451 Numerical Computations Lecture...

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