The Epsilon Modified Block-Pulse Function is used to approximate the solution of the second order initial value problem.

Abstract

The current study tackles the issue of converting second order initial value 
problems (IVPs) into a Volterra integral equation of the second type (VIE2) in order 
to approximate their solution. Since the IVPs may be converted to a lower triangular 
system of algebraic equations, we first solve them using Runge–Kutta of the forth
order technique (RK), after which we convert them into VIE2 and solve them using 
the εmodified block–pulse functions (εMBPFs) and their operational matrix. The 
suggested approach has an appropriate level of accuracy, as shown by numerical 
examples.