Abstract: 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 efficie...

The quadrature method of moments (QMOM) has emerged as a promising tool for the solution of population balance equations in the past few years. The QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments as well as nonlinear algebraic equations resulting from the quadrature approximation of moments. In this ...

A fractional time derivative is introduced into Burger’s equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equation...