New algorithm to solve nonlinear functional equations applying linearization then double discretization scheme (L.D.D)

Abstract

Solving functional nonlinear equations leads to the question: which to begin with, linearization or discretization? Recent papers confirmed that linearizing then discretizing (L.D) is better. In this paper, we develop a new numerical scheme that begins with the linearization phase and then, a double discretizations process (L.D.D). This new method gives a different theoretical framework where the convergence process is satisfied under some hypotheses. Many examples are offered to show the effectiveness of our new scheme. Starting with a comparison of the obtained numerical results with the results of a recently published research, moreover, applications to the system of nonlinear integro-differential equations. Obtained numerical results show that our (L.D.D) method is more efficient for solving nonlinear functional equations.