Numerical approximation to nonlinear delay-differential–algebraic equations with proportional delay using block boundary value methods

Abstract

This paper focuses on the numerical solutions of nonlinear delay-differential–algebraic equations with proportional delay, which are transformed into nonlinear delay- differential–algebraic equation with constant delay through exponential transformation. Block boundary value methods are extended to solve this type of equation, and their unique solvability, convergence, and stability are rigorously proved, respectively. The computational effectiveness of the methods and correctness of the theoretical result are illustrated through numerical examples.