The comparison between the DRBEM and DQM solution of nonlinear reaction-diffusion equation

Date

2011-10-01

Author

MERAL, GÜLNİHAL
Tezer, Münevver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

269
views

0
downloads

In this study, both the dual reciprocity boundary element method and the differential quadrature method are used to discretize spatially, initial and boundary value problems defined by single and system of nonlinear reaction-diffusion equations. The aim is to compare boundary only and a domain discretization method in terms of accuracy of solutions and computational cost. As the time integration scheme, the finite element method is used achieving solution in terms of time block with considerably large time steps. The comparison between the dual reciprocity boundary element method and the differential quadrature method solutions are made on some test problems. The results show that both methods achieve almost the same accuracy when they are combined with finite element method time discretization. However, as a method providing very good accuracy with considerably small number of grid points differential quadrature method is preferrable.

Subject Keywords

Modelling and Simulation, Applied Mathematics, Numerical Analysis

URI

https://hdl.handle.net/11511/44884

Journal

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

DOI

https://doi.org/10.1016/j.cnsns.2011.02.008

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes Meral, Gulnihal; Tezer, Münevver (Wiley, 2011-04-01) Three different time-integration schemes, namely the finite difference method (FDM) with a relaxation parameter, the least-squares method (LSM) and the finite element method (FEM), are applied to the differential quadrature (DQM) solution of one-dimensional nonlinear reaction-diffusion and wave equations. In the solution procedure, the space derivatives are discretized using DQM, which may also be used without the need of boundary conditions. The aim of the paper is to find computationally more efficient ti...
A coupled numerical scheme of dual reciprocity BEM with DQM for the transient elastodynamic problems Bozkaya, Canan (Wiley, 2008-11-12) The two-dimensional transient elastodynamic problems are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in spatial domain with the differential quadrature method (DQM) in time domain. The DRBEM with the fundamental solution of the Laplace equation transforms the domain integrals into the boundary integrals that contain the first- and the second-order time derivative terms. Thus, the application of DRBEM to elastodynamic problems results in a system of second...
An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows Demir, Medine (Elsevier BV, 2020-10-01) This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, includin...
A unified approach for the formulation of interaction problems by the boundary element method Mengi, Y; Argeso, H (Wiley, 2006-04-30) A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods....
On Stability of Linear Delay Differential Equations under Perron's Condition Diblík, J.; Zafer, A. (Hindawi Limited, 2011) The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.

Citation Formats

G. MERAL and M. Tezer, “The comparison between the DRBEM and DQM solution of nonlinear reaction-diffusion equation,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 3990–4005, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44884.