Evaluation of numerical integration schemes for a partial integro-differential equation

Abstract

Numerical methods are important in computational neuroscience where complex nonlinear systems are studied. This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integro-differential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficiency determined. Various ODE solvers in Matlab are used with the Fourier series method to solve the neural model, with an evaluation of the accuracy of the approximation versus the efficiency of the method. The two methodologies are then compared.