Mathematical Sciences: Studies in Numerical Solution of     Functional Differential Equations
{'Code': '03040101', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Alan Izenman', 'PO_EMAI': None, 'PO_PHON': None}
The purpose of this project is to study the numerical                      solution of functional differential equations and Volterra and                  Abel integral equations.  The principal investigator plans to                   examine the implementation of fully implicit one step methods                   and predictor-corrector methods for functional differential                     equations with step and step/order changing strategies based on                 the estimation of the local defect rather than the local                        discretization error.  This technique has been recently                         suggested by Enright in the context of ordinary differential                    equations.  Since the local defect depends on the approximate                   solution at the grid points as well as the interpolation scheme                 it is expected that, as in the case of ODE's, this technique                    will be more reliable than the technique based on the                           estimation of local discretization error alone.                                      The principal investigator  also plans to study stability                  properties of numerical methods for Volterra and Abel integral                  and integrodifferential equations with respect to various test                  equations.  These include convolution and nonconvolution test                   equations, equations with degenerate kernels and equations with                 completely positive kernels.  In many cases the application of                  numerical methods to these equations lead to recurrence                         equations with variable coefficients which are difficult to                     investigate.  Some novel approaches to the study the behaviour                  of solutions to these difference equations will also be                         investigated.
{'FirstName': 'Zdzislaw', 'LastName': 'Jackiewicz', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Zdzislaw Jackiewicz', 'EmailAddress': 'jackiewicz@asu.edu', 'NSF_ID': '000256076', 'StartDate': '06/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Arizona State University', 'CityName': 'TEMPE', 'ZipCode': '852813670', 'PhoneNumber': '4809655479', 'StreetAddress': '660 S MILL AVENUE STE 204', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arizona', 'StateCode': 'AZ', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'AZ04', 'ORG_UEI_NUM': 'NTLHJXM55KZ6', 'ORG_LGL_BUS_NAME': 'ARIZONA STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '9145', 'Text': 'SPECIAL PROGRAMS-RESERVE'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1989&All=true', 'xml': '8900411.xml'}