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

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.

Research highlights
► Nonlinear reaction–diffusion equations have practical applications in science.
► Their numerical solutions are important, since they often don’t have exact solutions.
► Two numerical schemes in space, DQM and DRBEM, are combined with FEM in time.
► DRBEM and DQM are compared through accuracy, computational load for the first time.
► The combination of DQM in space and FEM in time is preferrable.