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# Accession Number:

## ADA193697

# Title:

## Polynomial Definition of Discrete Field Points of Map of Diffusion Equation. Part 1.

# Descriptive Note:

## Memorandum rept.,

# Corporate Author:

## ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

# Report Date:

## 1988-03-01

# Pagination or Media Count:

##
40.0

# Abstract:

## The diffusion equation of Physics has been used to analyze unsteady heat transfer, boundary layer velocity distribution, long line electrical voltage fluctuation, and salt-solute penetration. There are two approaches to the problem statement and solution the one most widely used being transformation, and the other, finite difference techniques, employ variations of summing averages of term values established by unique methods. This report considers an averaging type solution in algebraic format. The final result consists of a series of discrete polynomials with rational coefficients which describe the dependent variable at each time-distance coordinate in the manner of the non-reflecting Schmidt plot. Essentially, the differential equation is recast as a finite difference expression which is transposed first to geometric and then to polynomial algebraic form. The polynomials, representing discrete solutions to the differential equations, are analyzed by differencing techniques whereby the numerical coefficients of common diagonal terms are found to be expressible in a generalized matrix.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#