A O(h sup 4) Cubic Spline Collocation Method for Quasilinear Parabolic Equations.
Technical rept. Sep-Dec 74,
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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A modified version of the usual cubic spline collocation method is proposed and analyzed for quasilinear parabolic problems. Continuous time estimates of order Oh sup 4 are obtained, via arguments based on certain discrete inner-products, for a uniform mesh and sufficiently smooth problems. Two types of collocation at the boundary are studied and shown to yield Oh sup 4 and Oh sup72 rates of convergence.
- Numerical Mathematics