ODE solvers using band-limited approximations

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ODE solvers using band-limited approximations

Abstract. We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit c and user selected accuracy ǫ, so that they integrate functions e, for all |b| ≤ c, with accuracy ǫ. Nodes of these quadratures do not concentrate excessively near the end points of an interval as those of the standard, polyno...

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Simple ODE Solvers - Error Behaviour

y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...

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ژورنال

عنوان ژورنال: Journal of Computational Physics

سال: 2014

ISSN: 0021-9991

DOI: 10.1016/j.jcp.2014.02.001