New Algorithm to Solve Nonlinear Functional Equations Applying Linearization then Double Discretization Scheme (L.D.D)



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.

Author Biographies

Ilyes Sedka, Laboratoire de Mathematiques Appliqu ´ ees et de Mod ´ elisation ´

Ilyes Sedka, is a third-year mathematics PhD student in University 8 May 1945 of Guelma Algeria.

Ammar Khellaf, Preparatory Class Department,National Polytechnic College of Constantine (Engineering College), Algeria

I am working on a research project which consists in developing numerical methods and techniques for solving non-linear equations and also used for solving spectral problems.

Mohamed Zine Aissaoui, University 8 May 1945 of Guelma, Algeria

Mohammed Zine Aissaoui, is a professor of mathematics, he has more than 20 years of experience in the field of scientific research.