Premium
Numerical solutions of fuzzy time fractional advection‐diffusion equations in double parametric form of fuzzy number
Author(s) -
Zureigat Hamzeh,
Ismail Ahmad Izani,
Sathasivam Saratha
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5573
Subject(s) - mathematics , partial differential equation , boundary value problem , parametric statistics , fuzzy logic , generalization , mathematical analysis , stability (learning theory) , machine learning , philosophy , linguistics , statistics , computer science
Fractional partial differential equations are a generalization of classical partial differential equations which can, in certain circumstances, give a better description of certain phenomena. In this paper, two implicit finite difference schemes are developed, analyzed, and applied to solve an initial boundary value problem involving fuzzy time fractional advection‐diffusion equation with fractional order 0< α ≤1. The fuzziness of the problem considered appears in the initial and boundary conditions. A computational mechanism is presented based on double parametric form of fuzzy number to transfer the problem from uncertain to crisp form. The stability of the proposed schemes is analyzed by means of the Von Neumann method and were found to be unconditionally stable. The scheme was applied to an example to illustrate the feasibility.