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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 41 Dec 7, 2011 Prof. Kamesh Madduri Class Overview RungeKutta methods Slides from textbook follow. 2 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods SingleStep 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 RungeKutta 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 SingleStep 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 higherorder singlestep 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 secondorder 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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