Interval Techniques for the Numerical Solution of Ordinary  Differential Equations.
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{'SignBlockName': 'S. Kamal Abdali', 'PO_EMAI': None, 'PO_PHON': None}
Ordinary differential equations (ODE's) are fundamental modeling tools          in many scientific and engineering application areas.  The models               typically involve systems of nonlinear ODE's which cannot be solved             analytically.  This, the interpretation of these models usually                 requires the computation of approximate numerical solutions.  Current           programs compute an estimate for the solution and (perhaps) an estimate         for the error.  However, the current codes only supply estimates; there         are no guarantees that the estimates are correct.                                                                                                               The co-investigators will evaluate existing interval techniques for             numerically solving ODE's, extend the techniques, and write a suite of          self-validating programs that compute interval inclusions of the                solution.  An inclusion is validated by appealing to appropriate                mathematical theorems.  In the case of numerical solutions of ODE's,            the logic of the program verifies the hypothesis of appropriate                 existence and uniqueness theorems.  Then the program can assert that a          solution exists and is contained in the computed interval.  The actual          computations use interval arithmetic to capture round-off and                   truncation errors.                                                                                                                                              The suite of programs written for this project will fill a role for             interval techniques similar to the role filled for point methods by             several programs written in the early 1970's.  It will serve both as a          fundamental tool for scientists and engineers and also as a test-bed            for further study and refinement of interval methods for ODE's.
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[{'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}, {'Code': '9120', 'Text': 'CROSS-DIRECTORATE PROGRAMS'}]
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