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


  • Muhammad Bilal Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
  • Shakoor Muhammad Abdul Wali Khan University Mardan, KP, Pakistan
  • Nekmat Ullah Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa,23200, Pakistan
  • Fazal Hanan Department of Mathematics, AIOU, Islamabad, Pakistan
  • Subahan Ullah Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa,23200, Pakistan




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.


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How to Cite

Bilal, M., Muhammad, S., Ullah, N., Hanan, F., & Ullah, S. (2022). Optimum solutions of partial differential equation with initial condition using optimization techniques. VFAST Transactions on Mathematics, 10(2), 118–136. https://doi.org/10.21015/vtm.v10i2.1170