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

DOI:
https://doi.org/10.1090/S0025-5718-1976-0408259-6

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