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We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = a ij (x)ux i x j + b i (x)ux i + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a… (More)

Efficient numerical algorithms are developed and analyzed that implement symmetric multilevel preconditioners for the solution of an orthogonal spline collocation (OSC) discretization of a Dirichlet boundary value problem with a non–self-adjoint or an indefinite operator. The OSC solution is sought in the Hermite space of piecewise bicubic polynomials. It… (More)

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