On the Effect of Boundary Conditions in Collocation by Polynomial Splines for the Solution of Boundary Value Problems in Ordinary Differential Equations |
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Authors: | GLADWELL I; MULLINGS D J |
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Institution: |
Department of Mathematics, University of Manchester Manchester 13
Department of Applied Mathematics and Computing Science, University of Sheffield Sheffield 10
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Abstract: | Consider the numerical solution of a boundary-value problemfor a differential equation of order m using collocation ofa polynomial spline of degree n m on a uniform mesh of sizeh. We describe several collocation schemes which differ onlyin the boundary collocation conditions and which include a "natural"spline collocation scheme. Taking account of derived asymptoticerror bounds most of which are, roughly speaking, of O(hn12m+1), we discuss the computational effectiveness of the variousschemes. |
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