@article{10.11648/j.acm.20221104.11,
  author = {Yanick Alain Servais Wellot and Gires Dimitri Nkaya},
  title = {Combination of Reduced Differential Transformation Method and Picard’s Principle},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {4},
  pages = {87-94},
  doi = {10.11648/j.acm.20221104.11},
  url = {https://doi.org/10.11648/j.acm.20221104.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221104.11},
  abstract = {In this paper, the combination of methods is used for the search for exact solutions, when they exist of mixed and non-mixed nonlinear partial differential equations. it is the combinate of reduced differential transform method and Picard principle. This combination gave us an algorithm that promotes the rapid convergence of the problem given the exact solution desired. Some complex physical behaviors can be described by mathematical expressions. These expressions can be nonlinear partial differential equations and sometimes mixed. For a better understanding of the physical phenomena associated with such partial differential equations, the exact solution, when it exists, is better indicated. However, by using classical analytical methods, the access or the obtaining of the exact solution is not always obvious. With some hybrid algorithms, the difficulties of accessing this exact solution can be difficult or almost impossible. Hence the coupling of some algorithms to reach the desired result. The objective of our work is the search for exact solutions when they exist of mixed and unmixed nonlinear partial differential equations. Although the reduced transform method has presented several interesting results, the difficulties of obtaining exact solutions have also been encountered. Thus, in this paper, a combination is used to find exact solutions, when they exist, of these types of partial differential equations. It is the combination of the reduced transform method and Picard's principle. This Picard principle, which uses the Adomian decomposition method, works as a method of successive approximations, approaching the problem by an iterative scheme. This combination gave us an algorithm that favors the fast convergence of the problem. Thus, the exact solutions of the selected problems are obtained.},
 year = {2022}
}

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TY  - JOUR
T1  - Combination of Reduced Differential Transformation Method and Picard’s Principle
AU  - Yanick Alain Servais Wellot
AU  - Gires Dimitri Nkaya
Y1  - 2022/07/22
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221104.11
DO  - 10.11648/j.acm.20221104.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 87
EP  - 94
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221104.11
AB  - In this paper, the combination of methods is used for the search for exact solutions, when they exist of mixed and non-mixed nonlinear partial differential equations. it is the combinate of reduced differential transform method and Picard principle. This combination gave us an algorithm that promotes the rapid convergence of the problem given the exact solution desired. Some complex physical behaviors can be described by mathematical expressions. These expressions can be nonlinear partial differential equations and sometimes mixed. For a better understanding of the physical phenomena associated with such partial differential equations, the exact solution, when it exists, is better indicated. However, by using classical analytical methods, the access or the obtaining of the exact solution is not always obvious. With some hybrid algorithms, the difficulties of accessing this exact solution can be difficult or almost impossible. Hence the coupling of some algorithms to reach the desired result. The objective of our work is the search for exact solutions when they exist of mixed and unmixed nonlinear partial differential equations. Although the reduced transform method has presented several interesting results, the difficulties of obtaining exact solutions have also been encountered. Thus, in this paper, a combination is used to find exact solutions, when they exist, of these types of partial differential equations. It is the combination of the reduced transform method and Picard's principle. This Picard principle, which uses the Adomian decomposition method, works as a method of successive approximations, approaching the problem by an iterative scheme. This combination gave us an algorithm that favors the fast convergence of the problem. Thus, the exact solutions of the selected problems are obtained.
VL  - 11
IS  - 4
ER  - 

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