On a new nonlinear integro-differential Fredholm-Chandrasekhar equation
DOI:
https://doi.org/10.5269/bspm.63023Abstract
This paper presents an analytical and numerical study of a new integro-differential Fredholm-Chandrasekhar equation of the second type. We suggest the conditions that ensure the existence and uniqueness of the nonlinear problem's solution. Then, we create a numerical technique based on the Nystr\"{o}m's method. The numerical application illustrates the efficiency of the proposed process.
References
1. M. Z. Aissaoui, M. C. Bounaya and H. Guebbai Analysis of a Nonlinear Volterra-Fredholm Integro-Differential Equation, Quaestiones Mathematicae, (2021) DOI: 10.2989/16073606.2020.1858991
2. K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework, Springer-Verlag, New York 2001.
3. M. C Bounaya, S. Lemita, M. Ghiat and M.Z Aissaoui, On a nonlinear integro-differential equation of Fredholm type, Computing Science and Mathematics, 13 (2021) 194–205.
4. J. Caballero, A. B. Mingarelli and K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative, Electron, J. Diff. Equat 57 (2006) 1–11.
5. S. Chandrasekhar, Radiative Transfar, Dover, New york 1960.
6. I. M. Esuabana, U. A. Abasiekwere, I. U. Moffat, Solution methods for integral equations - a survey, J. Math. Comput. Sci., 10 (2020), 3109–3142.
7. M. Ghiat and H. Guebbai, Analytical and numerical study for an integro-differential nonlinear volterra equation with weakly singular kernel, Comp. Appl. Math, 37 (2018) 4661–4674.
8. H. Guebbai, M. Z. Aissaoui, I. Debbar and B. Khalla, Analytical and numerical study for an integro-differential nonlinear Volterra equation, Appl. Math. Comp, 229 (2014) 367–373.
9. A. Khellaf, W. Merchela and S. Benarab, New numerical process solving nonlinear infinite dimensional equations. Computational and Applied Mathematics, 1 (2020) 1–15.
10. R. Kress, linear intergal equations, springer, New-york 2014.
11. P. Linz, Analytical and Numerical Methods for Volterra Equations. SIAM Studies in Applied Mathematics Philadelphia 1985.
12. K. Maleknejad, P. Torabi and R. Mollapourasl, Fixed point method for solving nonlinear quadratic Volterra integral equations, Computer and Mathematics with Applications 44 (2011) 5–28.
13. K. Maleknejad, P. Torabi and S. Sauter, Numerical solution of a non linear Volterra integral equation, Vitnam J. Math 44 (2016) 5–28.
14. S. Segni, M. Ghiat and H. Guebbai, New approximation method for Volterra nonlinear integro-differential equation, Asian-European Journal of Mathematics 12 (2019) 1950016.
15. V. Vougalter and V. Volpert, Solvability of some integro-differential equations with anomalous diffusion and transport Anal.Math.Phys. 11, (2021) 1-26.
2. K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework, Springer-Verlag, New York 2001.
3. M. C Bounaya, S. Lemita, M. Ghiat and M.Z Aissaoui, On a nonlinear integro-differential equation of Fredholm type, Computing Science and Mathematics, 13 (2021) 194–205.
4. J. Caballero, A. B. Mingarelli and K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative, Electron, J. Diff. Equat 57 (2006) 1–11.
5. S. Chandrasekhar, Radiative Transfar, Dover, New york 1960.
6. I. M. Esuabana, U. A. Abasiekwere, I. U. Moffat, Solution methods for integral equations - a survey, J. Math. Comput. Sci., 10 (2020), 3109–3142.
7. M. Ghiat and H. Guebbai, Analytical and numerical study for an integro-differential nonlinear volterra equation with weakly singular kernel, Comp. Appl. Math, 37 (2018) 4661–4674.
8. H. Guebbai, M. Z. Aissaoui, I. Debbar and B. Khalla, Analytical and numerical study for an integro-differential nonlinear Volterra equation, Appl. Math. Comp, 229 (2014) 367–373.
9. A. Khellaf, W. Merchela and S. Benarab, New numerical process solving nonlinear infinite dimensional equations. Computational and Applied Mathematics, 1 (2020) 1–15.
10. R. Kress, linear intergal equations, springer, New-york 2014.
11. P. Linz, Analytical and Numerical Methods for Volterra Equations. SIAM Studies in Applied Mathematics Philadelphia 1985.
12. K. Maleknejad, P. Torabi and R. Mollapourasl, Fixed point method for solving nonlinear quadratic Volterra integral equations, Computer and Mathematics with Applications 44 (2011) 5–28.
13. K. Maleknejad, P. Torabi and S. Sauter, Numerical solution of a non linear Volterra integral equation, Vitnam J. Math 44 (2016) 5–28.
14. S. Segni, M. Ghiat and H. Guebbai, New approximation method for Volterra nonlinear integro-differential equation, Asian-European Journal of Mathematics 12 (2019) 1950016.
15. V. Vougalter and V. Volpert, Solvability of some integro-differential equations with anomalous diffusion and transport Anal.Math.Phys. 11, (2021) 1-26.
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Published
2022-12-29
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Research Articles
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Direction Générale de la Recherche Scientifique et du Développement Technologique
Grant numbers C00L03UN410120220003
