Topic
Tridiagonal matrix algorithm
About: Tridiagonal matrix algorithm is a research topic. Over the lifetime, 1070 publications have been published within this topic receiving 21084 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, a fourth-order compact alternating direction implicit (ADI) method, based on the clasical Douglas-Gunn ADI method combined with Richardson's extrapolation technique, is proposed for solving 3-D unsteady convection-diffusion equations with discontinuous coefficients.
Abstract: In this article, a fourth-order compact alternating direction implicit (ADI) method, based on the clasical Douglas-Gunn ADI method combined with Richardson's extrapolation technique, is proposed for solving 3-D unsteady convection-diffusion equations with discontinuous coefficients. To achieve fourth-order temporal accuracy, a correction term that ensures the realization of extrapolation and reduces the splitting error is introduced. The scheme has unconditional stability and can be solved by the Thomas algorithm. Numerical experiments, including continuous/discontinuous coefficients cases, are conducted to verify the robustness and the high accuracy of this new method.
13 citations
TL;DR: In this paper, the authors constructed invariant regions in which they established the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions.
Abstract: The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions after the work of Kouachi (2004) on the system of reaction diffusion with a full 2-square matrix. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.
13 citations
TL;DR: An approximate factorisation explicit (AFE) algorithm for solving tridiagonal systems of equations iteratively on parallel processors is combined with a group finite element multigrid auxiliary potential solver for the incompressible Navier-Stokes equations.
13 citations
1 Sep 1990
TL;DR: This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, compute the eigenvalues of thetridiagonal matrix, improve the accuracy of an eigenvalue, and compute the corresponding eigenvector.
Abstract: This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, compute the eigenvalues of the tridiagonal matrix, improve the accuracy of an eigenvalue, and compute the corresponding eigenvector. 8 refs., 3 tabs.
13 citations
IBM1
13 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |