Spline-collocation with adaptive mesh grading for solving the stochastic collection equation
A numerical approach is given for solving the integro-differential partial equation \[ \partial /\partial tN(mt)=\int^{m/2}_{0}N(M,t)N(m-M,t)K(M,m-M)dM- N(m,t)\int^{\infty}\quad_{0}N(M,t)K(M,m)dM \] which arises in the study of water droplet coalescence. The equation is discretized using cubic B-splines and an adaptive mesh grading, and then collocation is used to obtain a system of ordinary differential equations whose solution is approximated using well-known numerical methods. Some examples were given to illustrate the effectiveness of this approach.
scientific article; zbMATH DE number 4070268