High convergence order methods with no derivatives for equations

Many applications from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of this equations are nondifferentiable. That is why a methodology is developed to handle in particular the solutions of such equations. However the methodology also applies to solve the differentiable equations. A particular method is utilized as a sample via which the method is described. However, the same methodology can be used on other methods utilizing the inverses of linear operators. Experiments further demonstrate the theory