A Semidiscrete Approximation Scheme for Neutral Delay-Differential Equations

Abstract

We consider an approximation scheme for systems of linear delay-differential equations of neutral type. The finite dimensional approximating systems are constructed with basis functions defined using linear splines, extending to neutral equations a scheme which had previously been defined only for retarded equations. A Trotter-Kato semigroup convergence result is proved, and numerical results are given to illustrate the qualitative behavior of the scheme.