Solving uncertain differential equations is a critical subject in the field of uncertainty theory, where uncertain differential equations are a sort of differential equations that involve Liu processes. Currently, considerable effort has been put into addressing this issue. Regrettably, analytic solutions to uncertain differential equations are not always accessible. As a result, several numerical methods have been investigated. However, numerical methods have certain limitations in terms of providing a continuous representation of the solution as well as more information about the solution. This paper will propose a novel algorithm based on the variational iteration method (VIM) for solving uncertain differential equations analytically or approximately analytically. The associated numerical experiments show that the proposed method is an efficient tool for solving uncertain differential equations.
LiuB.Some research problems in uncertainty theory, Journalof Uncertain Systems3(1) (2009), 3–10.
3.
LiuB.Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems2(1) (2008), 3–16.
4.
LiuB.Toward uncertain finance theory, Journal of UncertaintyAnalysis and Applications1(1) (2013), 1–15.
5.
LiZ., ShengY., TengZ., MiaoH.An uncertain differentialequation for SIS epidemic model, Journal of Intelligent &Fuzzy Systems33(4) (2017), 2317–2327.
6.
ZhangZ., YangX.Uncertain population model, Soft Computing24(4) (2020), 2417–2423.
7.
SunH., ShengY., CuiQ.An uncertain SIR rumor spreading model, Advances in Difference Equations2021(1) (2021).
8.
ChenX., LiuB.Existence and uniqueness theorem for uncertaindifferential equations, Fuzzy Optimization and Decision Making9(1) (2010), 69–81.
9.
YaoK., GaoJ., GaoY.Some stability theorems of uncertaindifferential equation, Fuzzy Optimization and Decision Making12(1) (2013), 3–13.
10.
YaoK., KeH., ShengY.Stability in mean for uncertaindifferential equation, Fuzzy Optimization and Decision Making14(3) (2015), 365–379.
11.
ShengY., WangC.Stability in p-th moment for uncertaindifferential equation, Journal of Intelligent & Fuzzy Systems26(3) (2014), 1263–1271.
12.
LiuH., KeH., FeiW.Almost sure stability for uncertaindifferential equation, Fuzzy Optimization and Decision Making13(4) (2014), 463–473.
13.
YaoK., LiuB.Parameter estimation in uncertain differentialequations, Fuzzy Optimization and Decision Making19(1) (2020), 1–12.
14.
ShengY., YaoK., ChenX.Least squares estimation in uncertaindifferential equations, IEEE Transactions on Fuzzy Systems28(10) (2020), 2651–2655.
15.
LiuY., LiuB.Estimating unknown parameters in uncertaindifferential equation by maximum likelihood estimation, SoftComputing26(6) (2020), 2773–2780.
16.
LioW., LiuB.Initial value estimation of uncertaindifferential equations and zero-day of COVID-19 spread in China, Fuzzy Optimization and Decision Making20(2) (2021), 177–188.
SaadatiR., DehghanaM., VaezpourS.M., SaraviM.Theconvergence of He’s variational iteration method for solvingintegral equations, Computers and Mathematics withApplications58(11) (2009), 2167–2171.
31.
LiuH., XiaoA., SuL.Convergence of variational iterationmethod for second-order delay differential equations, Journalof Applied Mathematics2013 (2013), 1–9.
32.
YangS., XiaoA., SuH.Convergence of the variational iterationmethod for solving multi-order fractional differential equations, Computers & Mathematics with Applications60(10) (2010), 2871–2879.
33.
AbbasbandyS., AllahviranlooT., DarabiP., SedaghatfarO., Mathematical and Computational Applications16(4) (2011), 819–829.
34.
AllahviranlooT., AbbasbandyS., Sh.S.Behzadi, Solvingnonlinear fuzzy differential equations by using fuzzy variationaliteration method, Soft Computing18 (2014), 2191–2200.
35.
InokutiM., SekineH., MuraT. General use of the Lagrange multiplier in nonlinear mathematical physics, in: S. Nemat-Nasser, ed.,Variational Methods in the Mechanics of Solids, Pergamon Press, 1980, pp. 156–162.
36.
FinlaysonB., The method of weighted residuals and variational principlesAcademic Press, New York,
1972.
