Open AccessNumerical Simulation for Fractional Percolation Equation
Author(s) -
I. I. Gorial
Publication year - 2021
Publication title -
mathematical modelling and engineering problems/mathematical modelling of engineering problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.26
H-Index - 11
eISSN - 2369-0747
pISSN - 2369-0739
DOI - 10.18280/mmep.080312
Subject(s) - fractional calculus , mathematics , derivative (finance) , consistency (knowledge bases) , exact solutions in general relativity , convergence (economics) , stability (learning theory) , boundary value problem , zero (linguistics) , mathematical analysis , computer science , discrete mathematics , financial economics , economics , economic growth , linguistics , philosophy , machine learning
The aims of this paper are to propose approach of explicit finite difference mathod (EFDM), clarify the problem the mixed fractional derivative in one-dimensional fractional percolation equation (O-DFPE), and the study of consistency, stability, and convergence methods. Use of estimated Grunwald estimation in the analysis of mixed fractional derivatives. However, the given method is successfully applied to the mixed fractional derivative classes with the initial condition (IC) and derivative boundary conditions (DBC). To illustrate the efficiency and validity of the proposed algorithm, examples are given and the results are compared with the exact solution. From the figures shown for the examples in this work, the approximate solution values given by the EFDM for the various grid points are equivalent to the exact solution values with high-precision approximation. To show the effectiveness of the proposed method, where the error between the EFDM and the exact method is zero, the fractional derivative was used with various and random values. Using the package MATLAB and MathCAD 12 Figures were introduced.