An Implicit Semianalytic Numerical Method for the Solution of Nonequilibrium Chemistry Problems.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION HAMPTON VA LANGLEY RESEARCH CENTER
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Most nonequilibrium chemistry problems, and many other physical phenomena, are modeled by systems of first order nonlinear ordinary or partial differential equations which for many applications are defined as stiff. These stiff systems are generally difficult to solve using classical techniques because of the rapid error growth and unless a very small time step is used the results can be greatly in error. However, because of the first order differential equation form these systems of equations can be solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution. From the sample problems solved using this technique the method is shown to be both computationally fast and relatively accurate. Chemistry, Mathematics, Numerical analysis.
- Numerical Mathematics