Spline-collocation with adaptive mesh grading for solving the stochastic collection equation

Abstract

The method of collocation using cubic B-splines and an adaptive mesh is applied to the solution of the partial integro-differential equation that describes the continuous mass spectrum of particles undergoing stochastic collection growth. Temporal discretization and a number of explicit and implicit linear multistep methods are employed to solve the system of ordinary differential equations. The numerical method is tested by solving model problems that describe the coalescence of particles for both single and double initial distributions. It is found that accurate solutions can be obtained using a small number of B-splines, and that adaptive mesh grading improves the accuracy of the solutions without needing additional nodal points.