Numerical solutions of distributed diffusion Hopfield neural network equations

A finite element method for numerical solutions of the systems governed by distributed models of Hopfield-type neural network equations is studied. When time keeps continuous and the spatial dimension is one, a semi-discrete algorithm for numerical solutions using quadratic interpolation functions is constructed, in which the Gauss-Legendre quadrature of numerical integrations of nonlinear term and Runge-Kutta method for solving ordinary differential equation are efficiently used. Finally, numerical simulations results obtained by Mathematica to show the scheme is stable.