General theory of the application of multistep methods to calculation of the energy of signals

Abstract

It is known that solving of many scientific and application problems can be regarded as the solving of integral equations with the variable boundaries. Among all the integral equations, the most popular ones are those in which one of the boundaries of the integral is fixed. Here, we investigate one particular case in which both boundaries of the integral equation are variable. Assuming that the boundaries of the integral are coincided on the module but have opposite signs, then for solving such equations, the use of symmetric methods is proposed. This paper constructs some general theories about the use of multistep symmetric methods to solve the Volterra integral equation with the symmetric variable boundaries and illustrates some results of the model equation.