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

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), 2021. Published by Science Publishing Group

Keywords

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

References
[1] Elbaz, E: Interactions fondamentales et structure de la mati`ere. Herman, Paris (2002).
[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.
Cite This Article
  • 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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    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
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Author Information
  • Faculty of Sciences, Joseph KI-ZERBO University, Ouagadougou, Burkina Faso

  • Faculty of Sciences, Dedougou University, Dedougou, Burkina Faso

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

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

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

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