A lagged diffusivity method for reaction–convection–diffusion equations with Dirichlet boundary conditions

Mezzadri, Francesco; Galligani, Emanuele

doi:10.1016/j.apnum.2017.09.009

Cited by 3 publications

(7 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proofs of these theorems and more information on B ρ,β can be found in [16]. In the literature it is also possible to find proofs of the convergence of the procedure for less general cases (e.g., see [2] for steady state reaction diffusion problems).…”

Section: Monotonicity Of the Finite-difference Operator And Convergenmentioning

confidence: 99%

“…This implementation follows the description in [2], with the difference that the inner systems are here solved by an inexact, simplified Newton iteration and that we use the correction on the initialization of tolerances presented in [16] and here summarized in Section 4.2. Then, we also briefly summarize the systems arising from the discretization and from the LDM and provide an algorithm which describes the entire procedure.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…The choice of the starting vectors is made so to start as close as possible to the solution of the system. Moreover, it also allows to write conveniently the linear system arising at each Newton iteration (e.g., see [16]). The stopping criteria, on the other hand, descend directly by the description of the LDM and by the choice of an inexact Newton iteration to solve the inner systems.…”

Section: Starting Vectors and Stopping Criteriamentioning

confidence: 99%

See 2 more Smart Citations

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

Mezzadri

Galligani

2017

Algorithms

Self Cite

View full text Add to dashboard Cite

Abstract:In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of the method itself. Moreover, we also analyze the behavior of the method in case of problems presenting boundary layers or blow-up solutions.

show abstract

Section: Monotonicity Of the Finite-difference Operator And Convergenmentioning

confidence: 99%

Section: Solution Proceduresmentioning

confidence: 99%

Section: Starting Vectors and Stopping Criteriamentioning

confidence: 99%

See 1 more Smart Citation

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

Mezzadri

Galligani

2017

Algorithms

Self Cite

View full text Add to dashboard Cite

show abstract

“…The main advantage of these techniques is that, at each lagging iteration, they linearize (al least partially) the nonlinear algebraic system, thus simplifying the computation of its Jacobian matrix. The most recent contribution [11] dealt with systems arising from general non-steady diffusion equations containing reaction and convection terms as well. The reader is referred to [11] also for a review of other papers on this topic.…”

Section: Introductionmentioning

confidence: 99%

“…The most recent contribution [11] dealt with systems arising from general non-steady diffusion equations containing reaction and convection terms as well. The reader is referred to [11] also for a review of other papers on this topic.…”

Section: Introductionmentioning

confidence: 99%

A nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms

Mezzadri

Galligani

2018

Adv Comput Math

Self Cite

View full text Add to dashboard Cite

We analyze an iterative procedure for solving nonlinear algebraic systems arising from the discretization of nonlinear, non-steady reaction-convection-diffusion equations with non-constant (and, in general, nonlinear) velocity terms. The basic idea underlying the procedure consists in lagging the diffusion and the velocity terms of the discretized system, which is thus partly linearized. After analyzing the discretized system and proving some results on the monotonicity of the operators and on the uniqueness of the solution, we prove sufficient conditions that ensure the convergence of this lagged method. We also describe the inner iteration and show how the weakly nonlinear systems arising at each lagged iteration can be solved efficiently. Finally, we analyze numerically the entire solution process by several numerical experiments.

show abstract

Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system

Sugathan

Awasthi

2020

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

A general numerical framework is designed for the two-dimensional convection–diffusion–reaction (CDR) system. The compatibility of differential quadrature and finite difference methods (FDM) are utilized for the formulation. The idea is to switch one numerical scheme to another numerical scheme without changing the formulation. The only requirement is to input the weighting coefficients associated with the derivative discretizations to the general algorithm. Three numerical schemes comprising combinations of differential quadrature and FDMs are studied using the general algorithm. Properties of numerical schemes and the algorithm are analyzed by using the simulations of two-dimensional linear CDR system, Burgers’ equation, and Brusselator model.

show abstract

A lagged diffusivity method for reaction–convection–diffusion equations with Dirichlet boundary conditions

Cited by 3 publications

References 25 publications

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

A nonlinearity lagging method for non-steady diffusion equations with nonlinear convection terms

Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system

Contact Info

Product

Resources

About