Cooperating Newton’s Method with Series Solution Method for Solving System of Linear Mixed Volterra-Fredholm Integral Equation of the Second Kind

  • Talaat I. Hasan Department of Mathematics, College of Basic Education, Salahaddin University, Erbil, Kurdistan Region, Iraq.
Keywords: Newton’s method, Series solution method, Taylor series, Volterra-Fredholm integral equations

Abstract

In this paper, for the 1st time, we use Newton’s method with series solution method (SSM) for solving system of linear mixed Volterra-Fredholm integral equations of the second kind (SLMVFIE-2). In this work, we use a new technique for studying the numerical solutions for SLMVFIE-2 which is Newton’s method with SSM, first solving this system using SSM and after that cooperation Newton’s method with SSM, suggesting an algorithm for the technique. The new results are achieved and some new theorems have proved for convergence of the method, several numerical examples are tested for illustrating the usefulness of the technique; the numerical results are obtained and compared with the exact solution, computing the least square error, and running times which are criterion of discussion. For programming the technique, we use general Matlab program.

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References

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Published
2019-05-13
How to Cite
1.
Hasan T. Cooperating Newton’s Method with Series Solution Method for Solving System of Linear Mixed Volterra-Fredholm Integral Equation of the Second Kind. cuesj [Internet]. 13May2019 [cited 28Jan.2022];3(1):27-3. Available from: https://journals.cihanuniversity.edu.iq/index.php/cuesj/article/view/43
Section
Research Article