16 research outputs found
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WebâTeaching â A Guide to Interactive Teaching for the WorldâWide Web by David W. Brooks, New York: Plenum, 1997. ISBN: 0â306â45552â8. Paperback, 214 pages. $30
Invariantization of numerical schemes using moving frames
This paper deals with a geometric technique to construct numerical schemes for differential equations that inherit Lie symmetries. The moving frame method enables one to adjust existing numerical schemes in a geometric manner and systematically construct proper invariant versions of them. Invariantization works as an adaptive transformation on numerical solutions, improving their accuracy greatly. Error reduction in the Runge-Kutta method by invariantization is studied through several applications including a harmonic oscillator and a Hamiltonian system.close111