Numerical solution of delay systems containing inverse time by hybrid functions

The hybrid functions consisting of general block-pulse functions and Legendre polynomials are presented to solve delay systems containing inverse time. The direct algorithm for a product of a matrix function and a vector function is given. The general operational matrix is introduced. The delay function and inverse time function are expanded by hybrid functions. The approximate solution of delay systems containing inverse time is derived. Numerical examples illustrate that the algorithms are applicable.