A novel approach for numeric study of 2D biological population model

In the present paper, the modified cubic B-spline differential quadrature method (MCB-DQM) has been implemented for the numerical computation of two-dimensional biological population model (BPM). The method is based on differential quadrature in which the weighting coefficients are computed by using MCB as a set of basis functions. We present three test problems to confirm the efficiency and accuracy of the method for BPM, which shows that the MCB-DQM solutions are in good agreement with the results obtained by the recent schemes: improved element-free Galerkin method by Zhang et al. and element-free kp-Ritz method by Cheng et al. The order of convergence of MCB-DQM for the solutions of BPM is shown to be quadratic.