Examining the Biological Species Steady-State Density Equation in Spaces with Different Dimensions

摘要

A computational solution to the integral equation in the biological spatial model is found. The numerical techniques that are used (the Nystrom and Neumann series methods, the latter being one of successive approximations) yield a reasonably accurate solution. An approach of moving from multidimensional equations to a one-dimensional equation for high-dimensional spaces is proposed. Explicit formulas for kernels when there are normal initial kernels are also proposed.