Discrete Least Squares Approximations for Ordinary Differential Equations.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The application of the least squares method, using C to the power q piecewise polynomials of order k m, K or m, q or m, for obtaining approximations to an isolated solution of a nonlinear m-th order ordinary differential equation, involves integrals which in practice need to be discretized. Using for this latter purpose the k-point Gaussian quadrature rule in each subinterval, the discrete least squares schemes obtained are close to collocation, on the same points, by piecewise polynomials from C to the power M-1.
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