Abstract
For a quasilinear parabolic problem in one space variable with nonlocal boundary conditions, we formulate and analyze the extrapolated Crank---Nicolson orthogonal spline collocation method with $$C^1$$ C 1 splines of degree $$\ge $$ ? 3. We establish an optimal order error bound in the discrete maximum norm in time and the continuous maximum norm in space. We present numerical results which confirm the theoretical analysis and exhibit superconvergence.
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