## Mesh Point Optimisation and Computational Considerations for a Collocation-projection Method |

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2q-1)th derivative 2r+mn+n Algorithm approximate solution approximating function B-spline basis B-spline Formulation Optimum B-spline matrix banded matrix boundary conditions boundary value problem Chapter CM CN CN CN CN collocation method Comp.Time Max.Err computational error condition number continuous derivatives convergence defined derivatives with respect differential equation DIMENSION divided difference error bounds error estimates expression finite FORMAT(1H Formulation Optimum Mesh GRAMIAN MATRIX Green's function H Eh Hence Hilbert space IMPLICIT REAL*8 A-H,O-Z inner product integral interval jth derivative Lemma linear operator equations matrix equation mesh points Mesh Uniform Mesh minimise n1 n Max.Err nonzero norm null space number of mesh number of Q obtain optimal optimised Optimum Mesh Uniform parameters polynomial positive definite programs projection method properties reproducing kernel RETURN END SUBROUTINE RKHS formulation rows satisfying selected set of mesh spanned splines subspace Test Problem theorem thesis vector