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
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Papers
TL;DR: In this article, a modified cubic B-spline based differential quadrature method was used to get numerical solutions of one dimensional reaction-diffusion systems such as linear reactiondiffusion system, Brusselator system, Isothermal system and Gray-Scott system.
Abstract: In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
50 citations
TL;DR: A simple, efficient, and stable mathematical algorithm for solving the tridiagonal matrix equation of the ADI-FDTD method is presented and it is demonstrated that, to obtain more accurate results for all the field components, the excitation function should be applied to both the first subiterations and the second subiteration, rather than forced in the firstSubiteration only.
Abstract: In this article two special considerations or notes on the implementation of the alternating direction implicit finite-difference–time-domain (ADI-FDTD) method are discussed. In particular, the two notes are (a) the mathematical algorithm used to solve the tridiagonal matrix equation, and (b) the way to apply the excitation. First, it is found that the ADI-FDTD method is not always stable if the algorithm (for solving the tridiagonal matrix equation) proposed in the book Numerical Recipes in C is adopted. Consequently, a simple, efficient, and stable mathematical algorithm for solving the tridiagonal matrix equation of the ADI-FDTD method is presented. Second, it is demonstrated that, to obtain more accurate results for all the field components, the excitation function should be applied to both the first subiteration and the second subiteration, rather than forced in the first subiteration only. The theory proposed in this article is validated through numerical examples. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 273–277, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10295
49 citations
TL;DR: In this paper, the authors have used a range of reaction orders with respect to both gaseous and solid reactants to analyze gas-solid non-catalytic (GSNC) reactions in porous particles.
Abstract: Gas–solid noncatalytic (GSNC) reactions in porous particles are analyzed employing volume reaction model (VRM). Both single-stage and two-stage models have been used in the work. Earlier analysis for such reactions was mostly restricted to the first-order reactions with respect to the gaseous component. The present work has used a range of reaction orders with respect to both gaseous and solid reactants. Front tracking method was employed for solving the moving boundary problem. Finite volume method (FVM) has been used for the first time for the analysis of GSNC reactions in porous particles, based on moving boundary zone models. The discretized equations are solved by tridiagonal matrix algorithm. The results for the first-order reaction agree well with the analytical solution. FVM solution compares well with other numerical method (integral transformation followed by orthogonal collocation). Numerical results have also been validated with reported experimental data for reduction of Magnetite by CO. FVM is thus established to be a suitable numerical method to solve GSNC reactions in porous particles employing VRM. The effects of different process parameters on the progress of reaction have also been assessed.© 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 1–11, 2003
49 citations
48 citations
47 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |