Accession Number : ADA185210

Title :   Numerical and Analytical Methods in Nonlinear Partial Differential Equations.

Descriptive Note : Final technical rept. 1 Nov 83-30 Apr 87,

Corporate Author : WYOMING UNIV LARAMIE

Personal Author(s) : Ewing, Richard E

PDF Url : ADA185210

Report Date : 30 Apr 1987

Pagination or Media Count : 18

Abstract : Complex physical phenomena involving chemically reacting systems or the transport of heat or fluids are often modeled by coupled systems of time-dependent, nonlinear partial differential equations. The difficulties in understanding the stability of the differential equation systems and in designing efficient, accurate numerical methods for their solution are widely recognized and were the focus of this research. We have worked on four general aspects of the analysis and numerical approximation of systems of partial differential equations. These areas of research are: (1) modeling aspects and stability analysis for nonlinear time-dependent partial differential equations; (2) use and analysis of finite element or finite difference methods to discretize coupled systems of nonlinear differential equations; (3) development of adaptive or local grid refinement capabilities to resolve local phenomena in large-scale applications; and (4) development of data structures, preconditioners, and efficient solution algorithms for large-scale problems on new computer architectures. Emphasis has been placed upon multiphase or multicomponent, transport-dominated flow processes with dynamic local phenomena. The research also involved a mix of analysis, algorithm development, and large-scale computation using newer computer architectures.

Descriptors :   *NUMERICAL ANALYSIS, *NONLINEAR DIFFERENTIAL EQUATIONS, *PARTIAL DIFFERENTIAL EQUATIONS, *HEAT TRANSMISSION, *FLUID FLOW, STABILITY, EFFICIENCY, TIME DEPENDENCE, APPROXIMATION(MATHEMATICS), ALGORITHMS, COMPUTER ARCHITECTURE

Subject Categories : Numerical Mathematics
      Thermodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE