Using (Direct Computation, Variation Iteration, Successive Approximation and Regularization) Methods to Solve Linear Fredholm Integral Equation and Comparison of These Methods

Authors

  • Najibullah Yousefi Teaching Assistant, Department of Higher Mathematics, Electromechanics Faculty, Kabul Polytechnic University, BaghBala, Kabul, AFGHANISTAN.
  • Hadia Jalal Sinior Teaching Assistant, Department of Higher Mathematics, Electromechanics Faculty, Kabul Polytechnic University, BaghBala, Kabul, AFGHANISTAN.
  • Laila Popalzai Sinior Teaching Assistant, Department of Higher Mathematics, Electromechanics Faculty, Kabul Polytechnic University, BaghBala, Kabul, AFGHANISTAN.

DOI:

https://doi.org/10.55544/jrasb.1.4.24

Keywords:

kernel, separable kernel, first and second kind, unknown function, Lagrange multiplier, variable, equivalent, converges, covert, effectively, correction function, same manner, approximation, real valued function, first approximation, Linear, consequent approximation

Abstract

Integral equation is the equation in which the unknown function to be determined, appears under integral sign as it presented in introduction.

I discussed about linear Fredholm integral equation in which it is one kind of integral equation and solved this equation by different methods (Direct Computation, Variational Iteration, Successive approximation and the Regularization methods and comparison of these methods in order to solve linear Fredholm integral equation).

 This paper has three parts:

First part: I introduced the Fredholm integral equation Second part is methods that is written above and on third part, I solved one example by these different methods and compare the methods.

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References

A.M. Wazwaz, first course in integral equation, World Scientific Publishing (2015)

Abdul. Majid Wazwaz, linear and nonlinear integral equation method and application, higher education Beijing (2011)

A.N. Tikhono. On the solution of incorrectly posed problem and the method of regularization, soviet Math (1963)

M. Rahman. Integral equation and their application, Dalhousie University, Canada, (2007)

M-Rahman, Integral equation and their Applications, WIT Press Southampton, Boston, (2007)

Ram. P. kamawal, Linear integral equation (theory and technique), acid free paper, Birkhauser Boston (1997)

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Published

2022-10-31

How to Cite

Yousefi, N., Jalal, H., & Popalzai, L. (2022). Using (Direct Computation, Variation Iteration, Successive Approximation and Regularization) Methods to Solve Linear Fredholm Integral Equation and Comparison of These Methods. Journal for Research in Applied Sciences and Biotechnology, 1(4), 171–175. https://doi.org/10.55544/jrasb.1.4.24

Issue

Vol. 1 No. 4 (2022): October Issue

Section

Articles

License

Copyright (c) 2022 Najibullah Yousefi, Hadia Jalal, Laila Popalzai

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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