About Exact Solution of Some Non Linear Partial Integro-differential Equations

Francis Bassono; Rasmané Yaro; Joseph Bonazebi Yindoula; Gires Dimitri Nkaya; Gabriel Bissanga

doi:doi:10.11648/j.acm.20211001.13

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About Exact Solution of Some Non Linear Partial Integro-differential Equations

Francis Bassono, Rasmané Yaro, Joseph Bonazebi Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga

Published in Applied and Computational Mathematics (Volume 10, Issue 1)

Received: 15 January 2021 Accepted: 24 February 2021 Published: 30 March 2021

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Abstract

Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.

Published in	Applied and Computational Mathematics (Volume 10, Issue 1)
DOI	10.11648/j.acm.20211001.13
Page(s)	19-29
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Partial Integro-differential Equation, Volterra-Fredholm Equation, SBA Method, Laplace SBA Method

References

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[2]	Guy, B-L: Elements of mathematical physics. Addison Wesley, Reading (2013).
[3]	Khajehnasiri A. A. Numerical Solution of Nonlinear 2D Volterra–Fredholm Integro-Differential Equations by Two-Dimensional Triangular Function. Int. Appl. Comput Math 2, 575-591 (2016).
[4]	A. Tari, “On the Existence Uniqueness and Solution of the Nonlinear Volterra Partial Integro-Differential Equations”, International Journal of Nonlinear Science, Vol. 16, No. 2, 152-163, (2013).
[5]	Tari, A, Rahimi, M. Y, Shahmad, S., Talati, F. Development of the Tau method for the numerical solution of two -dimentional linear Voltera integrodifferential equations. J. Comput Method Appl-math. 9 (4), 421-435 (2009).
[6]	Youssouf Pare, Youssouf Minoungou, Abdoul Wassiha Nebie “Resolution of nonlinear convection - diffusion - reaction equations of Cauchy’s kind by the Laplace SBA method”, EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 3, 2019, 771- 789.
[7]	Joseph Bonazebi Yindoula, Pare Youssouf, Gabriel Bissanga, Francis Bassono, Blaise Some. Application of the adomian decomposition method and the Some Blaise Abbo method to solving the diffusion-reaction equations. Advances in theorctical and applied mathematics, 9 (2): 97-104, 2014.
[8]	G. Nkaya, F. Bassono, R. Yaro, J. Bonazebi Yindoula “Application of the SBA method for solving the partial differential equation” 10 (6) (2018) 98-107.
[9]	O. Gonzalez J. Ruiz de Chavez and R. Bernal-Jaquez. Solution of the nonlinear kompaneets equation through the laplace-adomian decomposition method. Int. J.
[10]	Appl. Comput. Math, 3 (2): 489-504, 2017.
[11]	Bakodah HO. Anew modification of the Laplace- Adomian decomposition method for system of integral equations. J Am Sci. 2012; 8: 241-246.
[12]	Wazwaz A. The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations. Appl Math Comput. 2010; 216: 1304-1309.
[13]	Darania, P., Shali, J., Ivaz, K.: New computational method for solving some 2-dimensional nonlinear Volterra integro-differential equations. Numer. Algorithm 57, 125-147 (2011).
[14]	S. Ahmed and T. Elzaki. The solution of nonlinear volterra integro-differential equation of searel kind by combine Sumudu transforms and Adomian decomposition method. International Journal of Advanced and Inovative. Research 2 (2013) 90-93.

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APA Style

Francis Bassono, Rasmané Yaro, Joseph Bonazebi Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga. (2021). About Exact Solution of Some Non Linear Partial Integro-differential Equations. Applied and Computational Mathematics, 10(1), 19-29. https://doi.org/10.11648/j.acm.20211001.13

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ACS Style

Francis Bassono; Rasmané Yaro; Joseph Bonazebi Yindoula; Gires Dimitri Nkaya; Gabriel Bissanga. About Exact Solution of Some Non Linear Partial Integro-differential Equations. Appl. Comput. Math. 2021, 10(1), 19-29. doi: 10.11648/j.acm.20211001.13

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AMA Style

Francis Bassono, Rasmané Yaro, Joseph Bonazebi Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga. About Exact Solution of Some Non Linear Partial Integro-differential Equations. Appl Comput Math. 2021;10(1):19-29. doi: 10.11648/j.acm.20211001.13

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@article{10.11648/j.acm.20211001.13,
  author = {Francis Bassono and Rasmané Yaro and Joseph Bonazebi Yindoula and Gires Dimitri Nkaya and Gabriel Bissanga},
  title = {About Exact Solution of Some Non Linear Partial Integro-differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {1},
  pages = {19-29},
  doi = {10.11648/j.acm.20211001.13},
  url = {https://doi.org/10.11648/j.acm.20211001.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211001.13},
  abstract = {Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.},
 year = {2021}
}

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TY  - JOUR
T1  - About Exact Solution of Some Non Linear Partial Integro-differential Equations
AU  - Francis Bassono
AU  - Rasmané Yaro
AU  - Joseph Bonazebi Yindoula
AU  - Gires Dimitri Nkaya
AU  - Gabriel Bissanga
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211001.13
DO  - 10.11648/j.acm.20211001.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 19
EP  - 29
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211001.13
AB  - Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.
VL  - 10
IS  - 1
ER  -

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Author Information

Francis Bassono

Faculty of Sciences, Joseph KI-ZERBO University, Ouagadougou, Burkina Faso
Rasmané Yaro

Faculty of Sciences, Dedougou University, Dedougou, Burkina Faso
Joseph Bonazebi Yindoula

Faculty of Sciences and Technology, Marien NGOUABI University, Brazzaville, Congo
Gires Dimitri Nkaya

Faculty of Sciences and Technology, Marien NGOUABI University, Brazzaville, Congo
Gabriel Bissanga

Faculty of Sciences and Technology, Marien NGOUABI University, Brazzaville, Congo

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APA Style

Francis Bassono, Rasmané Yaro, Joseph Bonazebi Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga. (2021). About Exact Solution of Some Non Linear Partial Integro-differential Equations. Applied and Computational Mathematics, 10(1), 19-29. https://doi.org/10.11648/j.acm.20211001.13

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ACS Style

Francis Bassono; Rasmané Yaro; Joseph Bonazebi Yindoula; Gires Dimitri Nkaya; Gabriel Bissanga. About Exact Solution of Some Non Linear Partial Integro-differential Equations. Appl. Comput. Math. 2021, 10(1), 19-29. doi: 10.11648/j.acm.20211001.13

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AMA Style

Francis Bassono, Rasmané Yaro, Joseph Bonazebi Yindoula, Gires Dimitri Nkaya, Gabriel Bissanga. About Exact Solution of Some Non Linear Partial Integro-differential Equations. Appl Comput Math. 2021;10(1):19-29. doi: 10.11648/j.acm.20211001.13

Copy | Download

@article{10.11648/j.acm.20211001.13,
  author = {Francis Bassono and Rasmané Yaro and Joseph Bonazebi Yindoula and Gires Dimitri Nkaya and Gabriel Bissanga},
  title = {About Exact Solution of Some Non Linear Partial Integro-differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {1},
  pages = {19-29},
  doi = {10.11648/j.acm.20211001.13},
  url = {https://doi.org/10.11648/j.acm.20211001.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211001.13},
  abstract = {Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - About Exact Solution of Some Non Linear Partial Integro-differential Equations
AU  - Francis Bassono
AU  - Rasmané Yaro
AU  - Joseph Bonazebi Yindoula
AU  - Gires Dimitri Nkaya
AU  - Gabriel Bissanga
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211001.13
DO  - 10.11648/j.acm.20211001.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 19
EP  - 29
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211001.13
AB  - Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.
VL  - 10
IS  - 1
ER  -

Copy | Download