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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through
Control Structures
U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240
9. MATRIX SOLUTION AND NUMERICAL PROPERTIES OF THE
FINITE-DIFFERENCE SCHEME
The equations previously developed in sections 6 , 7, and 8
describe the flow and water-surface height in a network of open
channels. The nature of the stream system and the choices made by
the user determine which of the equations are included in a model
stream system. Once selected, these equations must be solved
simultaneously. The initial conditions define the flows and
water-surface heights at some starting time. The unknowns are the
flows and water-surface heights at the end of the next time step.
At the end of the computations for this time step, the unknowns
become the initial values for the following time step. Thus, the
equations of motion are solved many times. To be useful, a
computer program for simulation of unsteady flow in a network of
channels must include an efficient means for solving a system of
nonlinear equations.
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9.1 Newton's Iteration Method for Solution of Nonlinear
Equations
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9.2 Solution of a Sparse, Banded Matrix
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9.3 Stopping Criteria for Newton's Method
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9.4 Stability, Convergence, and Accuracy of the Solution
Scheme
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Last modified: Wed Nov 19 10:21:37 CST 1997