Statistical moments of the solution of the random Burgers-Riemann problem M. Cristina C. Cunha a F´abio A. Dorini a a Departamento de Matem´atica Aplicada, IMECC, UNICAMP, Cidade Universit´aria Zeferino Vaz, CP. 6065, 13083-970, Campinas, SP, Brazil. Abstract We solve Burgers’ equation with random Riemann initial conditions. The closed solution allows simple expressions for its statistical moments. Using these ideas we design an efficient algorithm to calculate the statistical moments of the solution. Our methodology is an alternative to the Monte Carlo method. The present approach does not demand a random numbers generator as does the Monte Carlo method. Computational tests are added to validate our approach. Key words: random Burgers’ equation, Monte Carlo method, Riemann problem, statistical moments, numerical methods for random partial differential equations. 1 Introduction When the data of a differential equation, the coefficients or the initial con- ditions, are random variables its solution is a random function; this kind of mathematical problem has been called a random differential equation. A great number of practical processes under current investigations falls on the stochas- tic modeling; we may quote the models in control, communications, economic systems, chemical kinetics, biosciences, statistical mechanics and spatial areas and so on. The methodology to understand and solve differential equations with uncertainties has stimulated studies under several points of view. Since the solution is a random function, one particular solution corresponding to a specific realization is not of concern: it is important to know the statisti- cal properties of the solution such as its mean, variance, or other statistical moments. Email addresses: cunha@ime.unicamp.br (M. Cristina C. Cunha), fabio.dorini@gmail.com (F´ abio A. Dorini). Preprint submitted to Elsevier Science 24 November 2007