Comparative analysis of numerical methods for the multidimensional Brusselator system
OMS-Vol. 3 (2019), Issue 3, pp. 262 – 272 Open Access Full-Text PDF
Harish Bhatt and Abhinandan Chowdhury
Abstract: 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 direction 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.