Author(s)

R. W. Johnson

Abstract

Progress on the development of B-spline collocation for the solution of differential model equations: a novel algorithm for adaptive knot insertion R.W. Johnson Idaho National Engineering and Environmental Laboratory, USA Abstract The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effectiveness and accuracy of B-spline collocation for solving differential equations include which points to use for collocation, what degree B-spline to use and what level of continuity to maintain. Success using higher degree B-spline curves having higher continuity at the knots, as opposed to more traditional approaches using orthogonal collocation, have recently been investigated

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