Numerical solutions of inverse spatial Lotka-Volterra systems

A numerical marching scheme is introduced for the recovery of the solutions and gradient distributions in a one-dimensional nonlinear system of parabolic partial differential equations with space dependent coefficients. In this inverse problem, only Cauchy noisy data at the active boundary is given and no information about the amount and/or character of the noise in the data is assumed. The error analysis for the algorithm is discussed and several numerical examples are presented.