Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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NUMERICAL SOLUTIONS OF NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY USING MADM AND VIM

  • Abed, Ayoob M. (Department of Mathematics, Thi Qar Directorates of Education Ministry of Education) ;
  • Younis, Muhammed F. (Department of Mathematics, Thi Qar Directorates of Education Ministry of Education) ;
  • Hamoud, Ahmed A. (Department of Mathematics, Faculty of Education and Science Taiz University)
  • Received : 2021.08.21
  • Accepted : 2021.12.10
  • Published : 2022.03.15
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Abstract

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

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References

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