Numerical solution of homogeneous Smoluchowski's coagulation equation

Abstract

Smoluchowski's equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. Analytical solutions for this equation, however, are known only for a very limited number of kernels. Therefore, numerical methods have to be used to describe the time evolution of the cluster-size distribution. A numerical technique is presented for the solution of the homogeneous Smoluchowski's coagulation equation with constant kernel. In this paper, we use Taylor polynomials and radial basis functions together to solve the equation. This method converts Smoluchowski's equation to a system of nonlinear equations that can be solved for unknown parameters. A numerical example with known solution is included to demonstrate the validity and applicability of the technique.

Keywords:

• the homogeneous Smoluchowski's coagulation equation
• radial basis functions
• meshless methods
• Newton–Raphson method

2000 AMS Subject Classifications :

• 65R20
• 82C05
• 65D30
• 65M70