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Tridiagonal fourth order approximations to general two-point nonlinear boundary value problems with mixed boundary conditions

Author: Robert S. Stepleman
Journal: Math. Comp. 30 (1976), 92-103
MSC: Primary 65L10
MathSciNet review: 0408259
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Abstract: This paper develops fourth order discretizations to the two-point boundary value problem \[ \begin {array}{*{20}{c}} {{y^{(2)}}(t) = f(t,y(t),{y^{(1)}}(t)),} \\ {{\alpha _0}y(0) - {\beta _0}{y^{(1)}}(0) = {\delta _0},\quad {\alpha _1}y(1) + {\beta _1}{y^{(1)}}(1) = {\delta _1}.} \\ \end {array} \] These discretizations have the desirable properties that they are tridiagonal and of "positive type".

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Keywords: Boundary value problems, mixed boundary conditions, fourth order discretization
Article copyright: © Copyright 1976 American Mathematical Society