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On dual Bernstein polynomials and stochastic fractional integro‐differential equations
Author(s) -
Sayevand Khosro,
Tenreiro Machado J.,
Masti Iman
Publication year - 2020
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.6667
Subject(s) - mathematics , algebraic equation , convergence (economics) , numerical analysis , dual (grammatical number) , bernstein polynomial , fractional calculus , differential equation , mathematical analysis , nonlinear system , art , physics , literature , quantum mechanics , economics , economic growth
In recent years, random functional or stochastic equations have been reported in a large class of problems. In many cases, an exact analytical solution of such equations is not available and, therefore, is of great importance to obtain their numerical approximation. This study presents a numerical technique based on Bernstein operational matrices for a family of stochastic fractional integro‐differential equations (SFIDE) by means of the trapezoidal rule. A relevant feature of this method is the conversion of the SFIDE into a linear system of algebraic equations that can be analyzed by numerical methods. An upper error bound, the convergence, and error analysis of the scheme are investigated. Three examples illustrate the accuracy and performance of the technique.