Comparative analysis of numerical methods for the multidimensional Brusselator system

Harish Bhatt, Department of Mathematics, Savannah State University, Savannah, Georgia 31404, USA.
2019 Open Journal of Mathematical Sciences  
This work is concerned with a comparative study of performances of meshfree (radial basis functions) and mesh-based (finite difference) schemes in terms of their accuracy and computational efficiency while solving multi-dimensional initial-boundary value problems governed by a nonlinear time-dependent reaction-diffusion Brusselator system. For computing the approximate solution of the Brusselator system, we use linearly implicit Crank-Nicolson (LICN) scheme, Peaceman-Rachford alternating
more » ... on implicit (ADI) scheme and exponential time differencing locally one dimensional (ETD-LOD) scheme as mesh-based schemes and multiquadric radial basis function (MQRBF) as a meshfree scheme. A few numerical results are reported.
doi:10.30538/oms2019.0069 fatcat:5xh2ercejraypkzth5a75csw7a