The linear two-point boundary-value problem on an infinite interval

Author:
T. N. Robertson

Journal:
Math. Comp. **25** (1971), 475-481

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1971-0303742-1

MathSciNet review:
0303742

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Abstract: A numerical method, using finite-difference approximations to the second-order differential equation, is given which tests the suitability of the finite point chosen to represent infinity before computing the numerical solution. The theory is illustrated with examples and suggestions for further applications of the method are presented.

**[1]**R. Bellman,*Stability Theory of Differential Equations*, McGraw-Hill, New York, 1953. MR**15**, 794. MR**0061235 (15:794b)****[2]**L. Fox,*Numerical Solution of Two-Point Boundary Value Problems in Ordinary Differential Equations*, Clarendon Press, Oxford, 1957. MR**0102178 (21:972)****[3]**H. B. Keller,*Numerical Methods for Two-Point Boundary-Value Problems*, Ginn-Blaisdell, Waltham, Mass., 1968. MR**37**#6038. MR**0230476 (37:6038)****[4]**F. W. J. Olver, ``Numerical solution of second-order linear difference equations,''*J. Res. Nat. Bur. Standards Sect. B*, v. 71B, 1967, pp. 111-129. MR**36**#4841. MR**0221789 (36:4841)****[5]**V. Pereyra, ``On improving an approximate solution of a functional equation by deferred corrections,''*Numer. Math.*, v. 8, 1966, 376-391. MR**34**#3814. MR**0203967 (34:3814)****[6]**R. S. Varga,*Matrix Iterative Analysis*, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR**28**#1725. MR**0158502 (28:1725)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0303742-1

Keywords:
Two-point boundary-value problem,
second-order linear differential equation,
finite-difference approximation,
condition at infinity

Article copyright:
© Copyright 1971
American Mathematical Society