Numerical solutions of ordinary differential equations using Spline-Integral Operator

In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order.