Implicit Schemes and LU Decompositions

Implicit Schemes and Lu Decompositions

Implicit methods for hyperbolic equations are analyzed using LU decompositions. It is shown that the inversion of the resulting tridiagonal matrices is usually stable even when diagonal dominance is lost. Furthermore, these decompositions can be used to construct stable algorithms in multidimensions. When marching to a steady state, the solution is independent of the time. Alternating direction...

Implicit and Semi - Implicit Schemes :

We formulate general guidelines to extend an explicit code with a great variety of implicit and semi-implicit time integration schemes. The discussion is based on their speciic implementation in the Versatile Advection Code, which is a general purpose software package for solving systems of non-linear hyperbolic (and/or parabolic) partial diierential equations, using standard high-resolution sh...

A I AA - 86 - 0 105 LU Implicit Schemes with Multiple Grids for the Euler Equations

History-based Schemes and Implicit Path Enumeration

The Implicit Path Enumeration Technique is often used to compute the WCET of control-intensive programs. This method does not consider execution paths as ordered sequences of basic blocks but instead as sets of basic blocks with their respective execution counts. This way of describing an execution path is adequate to compute its execution time, provided that safe individual WCETs for the block...

C++ Codes of Implicit Lu Algorithms for Absdll01

This report is devoted to some C++ codes implementing the implicit LU class algorithms for solving linear determined, and undetermined systems with n variables and m equations. A main program used in part of the numerical test is given in the last section.