Numerical Study Of Stochastic Supersensitiviy Of Generalized Burgers Equation

Supersensitivity and stochastic supersensitivity are important phenomenonof a class of nonlinear equations with essential theoretic and practical meanings.Subject to deterministic boundary inputs, Burgers equation and 2D generalizedBurgers equation exhibit supersensitivity while under random boundary inputsthey exhibit stochastic supersensitivity like that under deterministic boundaryinputs.According to di?erent boundary conditions, Supersensitivity and stochas-tic supersensitivity of Burgers equation are studied especially subject to uniformrandom boundary inputs.Also, 2D generalized Burgers equation's supersensitiv-ity and stochastic supersensitivity are studied and we focus on that subject touniform and Gaussian random boundary inputs.Chebyshev spectral collocationis employed to directly integrate equations to study supersensitivity and part ofresults are compared with asymptotic analysis and analytical results.Generalizedpolynomial chaos expansion is used to represent the random processes to trans-form the equation into a set of equations containing no random variable.that canbe solved by Chebyshev spectral collocation methods.As no analytical resultsare available, traditional Monte Carlo simulations are adopted.to validate thesolutions obtained from generalized polynomial chaos methods.