Solution of linearized boussinesq equation with stochastic boundaries and recharge
Budhi Sagar · Water Resources Research · 1979
By using the method of eigenfunction expansion a solution to the linearized Boussinesq equation with stochastic initial conditions, boundaries, and recharge is obtained. The solution is obtained explicitly in the form of two expressions, one for the expected value of the dependent variable and the other for its covariance. The inclusion of both the Neumann and the Dirichlet boundary conditions is considered. It is found that the expected value of the dependent variable is the same as the solution of the deterministic problem with expected values of the input stochastic quantities. An example of the use of the solution is presented. From the result of the example it is seen that the initial condition contributes a major portion to the standard deviation of the dependent variable.