Manuscript Title:

ANALYTICAL AND NUMERICAL SOLUTION USING VARIOUS ONE AND TWO STEPS METHOD OF GAUSS LOBATTO METHOD TO SOLVE FREDHOLM EQUATION

Author:

SAMI H. ALTOUM, MAHJOUB A. ELAMIN, HA ELSAYIR, NEMAAT HAMID ISMAIEL

DOI Number:

DOI:10.5281/zenodo.15208695

Published : 2025-04-10

About the author(s)

1. SAMI H. ALTOUM - AL-Qunfudhah University College, Umm Al-Qura University, Department of Mathematics- KSA.
2. MAHJOUB A. ELAMIN - University of Tabuk, University College of Umluj, Department of Mathematics- KSA.
3. HA ELSAYIR - Department of Mathematics, University College of Qunfudhah, Umm Al-Qura University, Makkah, KSA.
4. NEMAAT HAMID ISMAIEL - University of Tabuk, University College of Umluj, Department of Mathematics- KSA.

Full Text : PDF

Abstract

In this paper, we discuss numerical experiment of absolute stability of various one and two steps method for ODEs and Fredholm equation. The Gauss Lobatto method for approximating the value of the integrals presented. Two and one dimensional case of spectral element method are presented. The proposed method provides the solution in terms of convergent series with easily computable components, as well as it possesses main advantage as compared to other existed methods.


Keywords

Numerical Method, Fredholm Equation, Gauss Lobatto Method.