an adaptive physics -based method for solution of wave motion problem in one dimension

in this paper an adaptive physics -based method is developed for solving wave motion problem in one dimension the solution of the problem has two main parts in the first part after discretization of the domain a physics -based method is developed considering the conservation of mass and the balance of momentum in the second part adaptive points are determined using wavelet theory this part is well done using D-D wavelets introduced by deslauries and dubuc. solving the problem in the first step the domain of the problem is discretized by the same cells considering the loading and characteristics of the structure.