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Optimum solutions of partial differential equation with initial condition using optimization techniques

Author(s)
Muhammad Bilal Department of Mathematical Sciences,BUITEMS, Quetta 87300,Pakistan
Shakoor Muhammad Department of Mathematics, Abdul Wali Khan University Mardan,Khyber Pakhtunkhwa,23200,Pakistan
Nekmat Ullah Department of Mathematics, Abdul Wali Khan University Mardan,Khyber Pakhtunkhwa,23200,Pakistan
Fazal Hanan Department of Mathematics,AIOU, Islamabad,Pakistan
Subhan Ullah Department of Mathematics, Abdul Wali Khan University Mardan,Khyber Pakhtunkhwa,23200,Pakistan
Abstract
This paper proposes a new minimization technique for the solutions of partial differential equation with initial conditions. The proposed procedure is used to minimize the obtained solutions through any numerical technique. For the minimization process, Non-linear Nelder-Mead Simplex algorithm and genetic algorithm are used as optimization techniques. The designed partial differential equation has been calculated as an error function for the minimization process. Both Non-linear Nelder-Mead Simplex and genetic algorithm guarantees the minimization of nonlinear partial differential equation with initial conditions. The resultant technique has a global validity for the solutions minimization of partial differential equations. Non-linear Nelder-Mead simplex showed better performance than genetic algorithm when tested on numerical instances.
Publication Details
Page(s) 118-136
DOI DOI not available
Published Journal: VFAST Transactions on Mathematics, Volume: 10, Issue: 2, Year: 2022

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Keywords
Genetic Algorithm, Nelder Mead Simplex algorithm, Write Subject Classification separated by comma, unconstrained optimization Subject Classification, Nonlinear PDE
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