Implicit schemes and $LU$ decompositions
Authors:
A. Jameson and E. Turkel
Journal:
Math. Comp. 37 (1981), 385397
MSC:
Primary 65M10; Secondary 65F05
DOI:
https://doi.org/10.1090/S00255718198106287029
MathSciNet review:
628702
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Abstract: Implicit methods for hyperbolic equations are analyzed by constructing LU factorizations. It is shown that the solution of the resulting tridiagonal systems in one dimension is well conditioned if and only if the LU factors are diagonally dominant. Stable implicit methods that have diagonally dominant factors are constructed for hyperbolic equations in n space dimensions. Only two factors are required even in three space dimensions. Acceleration to a steady state is analyzed. When the multidimensional backward Euler method is used with large time steps, it is shown that the scheme approximates a NewtonRaphson iteration procedure.

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Article copyright:
© Copyright 1981
American Mathematical Society