On a New Approach to the Computational Solution of Partial Differential Equations

Richard Ernest Bellman, Robert E. Kalaba, Bella Kotkin

ResearchPublished 1962

The most versatile and frequently used method for numerically solving partial differential equations is that of approximation by difference equations. While the method has the advantages of conceptual simplicity, wide applicability, and ready suitability for digital computation, it also has the disadvantages of a predilection toward instability and of a frequent requirement for large storage capacity and excessive computing time. This Memorandum describes a modified approach that may be superior in some instances. Considering a particular equation, the usual difference approximation is replaced with a recurrence relation that clearly preserves such properties as boundedness and nonnegativity and that tends to the solution in the limit.

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  • Copyright: RAND Corporation
  • Availability: Available
  • Year: 1962
  • Print Format: Paperback
  • Paperback Pages: 12
  • Paperback Price: $20.00
  • Document Number: RM-3133-PR

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RAND Style Manual
Bellman, Richard Ernest, Robert E. Kalaba, and Bella Kotkin, On a New Approach to the Computational Solution of Partial Differential Equations, RAND Corporation, RM-3133-PR, 1962. As of September 24, 2024: https://www.rand.org/pubs/research_memoranda/RM3133.html
Chicago Manual of Style
Bellman, Richard Ernest, Robert E. Kalaba, and Bella Kotkin, On a New Approach to the Computational Solution of Partial Differential Equations. Santa Monica, CA: RAND Corporation, 1962. https://www.rand.org/pubs/research_memoranda/RM3133.html. Also available in print form.
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