Open AccessA novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
Author(s) -
Seddigheh Banihashemi,
Hossein Jafaria,
Afshin Babaei
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021025
Subject(s) - collocation (remote sensing) , nonlinear system , legendre polynomials , mathematics , collocation method , constant (computer programming) , orthogonal collocation , stochastic differential equation , differential equation , mathematical analysis , computer science , ordinary differential equation , physics , quantum mechanics , machine learning , programming language
In present work, a step-by-step Legendre collocation method is employed to solve a class of nonlinear fractional stochastic delay differential equations (FSDDEs). The step-by-step method converts the nonlinear FSDDE into a non-delay nonlinear fractional stochastic differential equation (FSDE). Then, a Legendre collocation approach is considered to obtain the numerical solution in each step. By using a collocation scheme, the non-delay nonlinear FSDE is reduced to a nonlinear system. Moreover, the error analysis of this numerical approach is investigated and convergence rate is examined. The accuracy and reliability of this method is shown on three test examples and the effect of different noise measures is investigated. Finally, as an useful application, the proposed scheme is applied to obtain the numerical solution of a stochastic SIRS model.