Resumen
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 $Lu=\sum a_{ij}(x)u_{x_ix_j}+\sum b_i(x) u_{x_i}+c(x)u$. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the resulting algorithm has a convergence rate independent of the partition step size. We solve a problem with the preconditioner using an efficient direct matrix decomposition algorithm. On a uniform N × N partition, the cost of the algorithm for computing the collocation solution within a tolerance $\epsilon$ is O$(N^{2}\ln N |\ln \epsilon|)$.