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Approximate solution of the differential equation $ y\sp{''}=f(x,\,y)$ with spline functions

Author: Gh. Micula
Journal: Math. Comp. 27 (1973), 807-816
MSC: Primary 65L05
Corrigendum: Math. Comp. 29 (1975), 673-674.
Corrigendum: Math. Comp. 29 (1975), 673-674.
MathSciNet review: 0331789
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Abstract: An approximate spline is constructed for the solution of Cauchy's problem regarding a second-order differential equation. The existence, uniqueness and convergence of the approximate spline solution are investigated.

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Keywords: Differential equation, Cauchy problem, spline function, consistency relations, fixed point, discrete multistep method, stable method, convergence
Article copyright: © Copyright 1973 American Mathematical Society