Successive approximations for the solution of second order advanced

For the initial value problem associated with second order advanced differential equation on Banach space, it is constructed a numerical method to approximate the solution. The method uses the sequence of Picard successive approximations and the trapezoidal quadrature rule (adapted for Lipschitzian functions with values in Banach spaces). For the initial value problem associated with second order advanced differential equation on Banach space, it is constructed a numerical method to approximate the solution. The method uses the sequence of Picard successive approximations and the trapezoidal quadrature rule (adapted for Lipschitzian functions with values in Banach spaces).