On the numerical solution of elliptic difference equations

Author:
John W. Sheldon

Journal:
Math. Comp. **9** (1955), 101-112

MSC:
Primary 65.0X

MathSciNet review:
0074929

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References | Similar Articles | Additional Information

**[1]**L. F. Richardson, ``The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to stresses in a masonry dam,'' Roy. Soc., London,*Phil. Trans.*, Sec. A, v. 210, 1910, p. 307-357.**[2]**David Young,*Iterative methods for solving partial difference equations of elliptic type*, Trans. Amer. Math. Soc.**76**(1954), 92–111. MR**0059635**, 10.1090/S0002-9947-1954-0059635-7**[3]**Stanley P. Frankel,*Convergence rates of iterative treatments of partial differential equations*, Math. Tables and Other Aids to Computation**4**(1950), 65–75. MR**0046149**, 10.1090/S0025-5718-1950-0046149-3**[4]**James D. Riley,*Iteration procedures for the Dirichlet difference problem*, Math. Tables and Other Aids to Computation**8**(1954), 125–131. MR**0064493**, 10.1090/S0025-5718-1954-0064493-4**[5]**George Shortley,*Use of Tschebyscheff-polynomial operators in the numerical solution of boundary-value problems*, J. Appl. Phys.**24**(1953), 392–396. MR**0055042****[6]**David Young,*On Richardson’s method for solving linear systems with positive definite matrices*, J. Math. Physics**32**(1954), 243–255. MR**0060306****[7]**D. Young,*op. cit.*, reference 2, p. 93.**[8]**D. Young,*op. cit.*, p. 108.**[9]**D. Young,*op. cit.*, section 4.**[10]**D. Young,*op. cit.*, p. 96.**[11]**A. C. Aitken,*Studies in practical mathematics. V. On the iterative solution of a system of linear equations*, Proc. Roy. Soc. Edinburgh. Sect. A.**63**(1950), 52–60. MR**0036086****[12]**D. Young,*op. cit.*, reference 2, p. 103.**[13]**The International Business Machines Company Type 701 Electronic Data Processing Machines located at the IBM Scientific Computing Service, 590 Madison Ave., New York City, N. Y.**[14]**John Sheldon and L. H. Thomas,*The use of large scale computing in physics*, J. Appl. Phys.**24**(1953), 235–242. MR**0053602**

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DOI:
https://doi.org/10.1090/S0025-5718-1955-0074929-1

Article copyright:
© Copyright 1955
American Mathematical Society