Published September 6, 2022 | Version v1

An optimization approach for fractional reaction-diffusion equations with nonlocal boundary conditions

  • 1. Department of Mathematics, Faculty of Mathematical sciences, Alzahra University, Tehran, Iran

Description

In this paper, we present an optimization approach for solving fractional reaction-diffusion equations with nonlocal boundary conditions. To receive the desired goal, we applied a modified operational matrix of integration and an operational matrix of fractional derivative. At last, to demonstrate the accuracy of the method, we present an example.

Files

H-Dehestani.pdf

Files (414.8 kB)

Name Size
md5:0efe600507bb1f6160569a33d9b43f22
414.8 kB Preview Download

Additional details

References

  • Shahmorad, S., Borhanifar, A., Soltanalizadeh, B. An approximation method based on matrix formulated algorithm for the heat equation with nonlocal boundary conditions. Comput. Methods Appl. Math. 12(1) (2012) 92–107.
  • A. Borhanifar, S. Shahmorad, E. Feizi, A matrix formulated algorithm for solving parabolic equations with nonlocal boundary conditions. Numer Algorithms, 74(4) (2017) 1203–1221.
  • H. Dehestani, Y. Ordokhani, Composition of Euler scaling functions with the optimization method for fractional hyperbolic and reaction-diffusion equations with nonlocal boundary conditions, Numer Funct Anal Optim, https://doi.org/10.1080/01630563.2022.2056898
  • M. K. Kadalbajoo, A. Kumar, L. P. Tripathi, A radial basis functions based finite differences method for wave equation with an integral condition. Appl Math Comput, 253 (2015) 8–16.
  • H. Dehestani, Y. Ordokhani, M. Razzaghi, An improved numerical technique for distributed-order time-fractional diffusion equations, Numer Methods Partial Differential Eq, 37 (2021) 2490–2510.
  • O. Omer, A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin–Bona–Mahony–burgers equation, Comput Math Appl, 74(12) (2017) 3042-–3057.