Approximating a Retarded-Advanced Differential Equation Using Radial Basis Functions

摘要

In last years we have got the approximation of the solution of a linear mixed type functional differential equation, considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering a polynomial basis. The present work introduces a numerical scheme using collocation and radial basis functions to solve numerically the non-linear mixed type equation with symmetric delay and advance. The results are similar using collocation, B-splines and exponential radial functions. The preliminary results are promising, but more simulations using different basis of radial functions are needed.