exponential finite difference technique for solving partial differential equations
An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.
- OSTI ID:
- 6031139
- Report Number(s):
- N-87-24930; NASA-TM-89874; E-3544; NAS-1.15:89874; AVSCOM-TR-87-C-19
- Resource Relation:
- Other Information: M.S. Thesis - Toledo Univ., Ohio
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PARTIAL DIFFERENTIAL EQUATIONS
FINITE DIFFERENCE METHOD
ALGORITHMS
CARTESIAN COORDINATES
COUETTE FLOW
DIFFUSION
HEAT TRANSFER
LAMINAR FLOW
NUMERICAL ANALYSIS
THERMAL CONDUCTIVITY
COORDINATES
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
FLUID FLOW
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
VISCOUS FLOW
420400* - Engineering- Heat Transfer & Fluid Flow
657000 - Theoretical & Mathematical Physics