VOLTERRA INTEGRODIFFERENTIAL EQUATIONS AND RUNGE-KUTTA METHODS

Abstract

The following Volterra Integro-Differential Equations are examined for their nonlinear stability and convergence includes using RK methods of order 4.
where (1) has a distinctive solution and f, g, and φ are generic functions. An inner product ⟨⋅,⋅⟩ and the generated norm‖⋅‖ in R exist, and y(t) and τ is a not negative delay term. As a result, φ:[-τ,0]→ R andf∶ [0,T]→ R satisfy the conditions as follows: