Different Time Schemes with Differential Quadrature Method in Convection-Diffusion-Reaction Equations

Geridönmez B.

2nd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2021, Salamanca, Spain, 1 - 02 July 2021, vol.384, pp.103-111 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 384
  • Doi Number: 10.1007/978-3-030-96401-6_9
  • City: Salamanca
  • Country: Spain
  • Page Numbers: pp.103-111
  • Keywords: Convection-diffusion-reaction, Differential quadrature method, Time schemes
  • TED University Affiliated: Yes


© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.In this study, two-dimensional, unsteady convection-diffusion and convection-diffusion-reaction equations are numerically investigated with different time schemes. In the governing equations, the space derivatives are approximated by differential quadrature method (DQM) which gives highly accurate results using small number of grid points and the time derivatives are handled by different time schemes. The distribution of nodes is achieved by non-uniform Gauss-Chebyshev-Lobatto (GCL) grid points. The problems having the exact solutions are chosen to check the best error behavior. Computational cost in view of central processing unit time and the efficiency of different time schemes in terms of errors are examined. As expected, explicit time schemes need smaller time increments while implicit time schemes enable one to use larger time increments. In each chosen problems, Adams-Bashforth-Moulton and Runge-Kutta of order four exhibit the best error behavior.