Analytical time-stepping solution of the discretized population balance equation

Jama, Mohamed; Zhao, Wenzhu; Ahmad, Waqar; Buffo, Antonio; Alopaeus, Ville

doi:10.1016/j.compchemeng.2020.106741

Cited by 5 publications

(1 citation statement)

References 45 publications

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“…The focus of this paper is on the numerical solution of the fractal-fractional two-dimensional Fredholm-Volterra integro-differential equations. The Fredholm-Volterra integro-differential equations have interesting applications in physics, mechanics, and applied sciences, [15][16][17][18] but researchers are looking to introduce a simple numerical method to solve these equations with high accuracy. The computational approach in solving proposed equations has conspicuous roles, which we introduce some of them.…”

Section: Introductionmentioning

confidence: 99%

Developing the discretization method for fractal‐fractional two‐dimensional Fredholm–Volterra integro‐differential equations

Dehestani

Ordokhani

2021

Math Methods in App Sciences

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This paper contains the computational approach based on Mott polynomials together with the two-dimensional Legendre-Gauss (LG) quadrature rule for fractal-fractional two-dimensional Fredholm-Volterra (FF-2D-FV) integro-differential equations. Furthermore, we applied the modified operational matrices of integration and fractional derivative in the process of the numerical algorithm to get the approximate solution with high accuracy.The fractal-fractional derivative is defined in the Atangana-Riemann-Liouville sense. Besides, we estimate the error of the method in Sobolev space. Ultimately, to prove the theoretical claim, we represent the numerical results in the form of tables and diagrams.

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Section: Introductionmentioning

confidence: 99%