Abstract: The vibration of rod system in the elastic continuous medium is a problem which is often met and also a composite solution problem of elastic dynamics and structural dynamics. It seems rather difficult and complex to find solutions by general method. Using Lagrangian method of multipliers, we give here the generalized functionals concerning this kind of plane problem and show how to apply the method presented through examples.

Key words: shallow water flow, pollutant diffusion, TVD scheme, finite-volume method, numerical simulation