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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Implicit schemes and $LU$ decompositions
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by A. Jameson and E. Turkel PDF
Math. Comp. 37 (1981), 385-397 Request permission


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 Newton-Raphson iteration procedure.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 385-397
  • MSC: Primary 65M10; Secondary 65F05
  • DOI:
  • MathSciNet review: 628702