Discontinuous Legendre wavelet Galerkin method for reaction-diffusion equation

This paper proposes a novel numerical method, that is, discontinuous Legendre wavelet Galerkin technique for solving reaction-diffusion equation (RDE). Specifically, variational formulation and corresponding numerical fluxes of this type equation are devised by utilizing the advantages of both Legendre wavelet bases and discontinuous Galerkin approach. Furthermore, adaptive algorithm, stability and error analysis of this method have been discussed. Especially, the distinctive features of the presented approach are easy to cope with a variety of boundary conditions and able to effectively approximate solution of the RDE with less execution and storage space. Finally, numerical tests affirm better accuracy for a range of benchmark problems and demonstrate the validity and utility of this approach.