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...

New integrability properties of a family sequences ordinary differential equations, which contains the Riccati and Abel chains as most simple sequences, are studied. The determination n generalized symmetries nth-order equation in each chain provides, without any kind integration, n-1 functionally independent first integrals equation. A remaining integral arises by quadrature using Jacobi last ...