In this paper we discuss the existence of a solution of a first order neutral differential equation with piecewise constant argument. We extend the method of Chaplygin’s sequence to obtain two sided bounds for the solution. These bounds are in the form of sequences of functions which are solutions of associated linear neutral differential equations with piecewise constant argument. This construction of monotonic sequences of upper and lower functions approximate, with increasing accuracy, the desired solution of the neutral differential equation with piecewise constant argument. Further we show that these sequences converge uniformly and monotonically to the unique solution of the equation.The error estimate obtained is better than the corresponding one for ordinary differential equations.
Kumari, Mamta and Valaulikar, Y. S.
On Chaplygin’s Method For First Order Neutral Differential Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 11.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/11