Minimising truncation error in finite difference approximations to ordinary differential equations

Author:
M. R. Osborne

Journal:
Math. Comp. **21** (1967), 133-145

MSC:
Primary 65.61

DOI:
https://doi.org/10.1090/S0025-5718-1967-0223107-X

MathSciNet review:
0223107

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Abstract: It is shown that the error in setting up a class of finite difference approximations is of two kinds: a quadrature error and an interpolation error. In many applications the quadrature error is dominant, and it is possible to take steps to reduce it. In the concluding section an attempt is made to answer the question of how to find a finite difference formula which is best in the sense of minimising the work which has to be done to obtain an answer to within a specified tolerance.

**[1]**J. T. Day, ``A one-step method for the numerical solution of second order linear ordinary differential equations,''*Math. Comp.*, v. 18, 1964, pp. 664-668. MR**29**#5385. MR**0168121 (29:5385)****[2]**M. R. Osborne, ``A method for finite-difference approximation to ordinary differential equations,''*Comput. J.*, v. 7, 1964, pp. 58-65. MR**31**, #5338. MR**0181109 (31:5338)****[3]**M. R. Osborne & S. Michaelson, ``The numerical solution of eignvalue problems in which the eigenvalue parameter appears nonlinearly, with an application to differential equations,''*Comput. J.*, v. 7, 1964, pp. 66-71. MR**31**#4167. MR**0179930 (31:4167)****[4]**J. Hersch, ``Contribution a la méthode des équations aux différences,''*Z. Angew. Math. Phys.*, v. 9a, 1958, pp. 129-180. MR**21**#1708. MR**0102923 (21:1708)****[5]**M. E. Rose, ``Finite difference schemes for differential equations,''*Math. Comp.*, v. 18, 1964, pp. 179-195. MR**32**#605. MR**0183123 (32:605)**

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DOI:
https://doi.org/10.1090/S0025-5718-1967-0223107-X

Article copyright:
© Copyright 1967
American Mathematical Society