The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context extended theories gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives metric tensor. finding such solutions, make use an order reduction technique based on a perturbative approach. Reducing second-order, are able find solutions whic...

In this paper, we present a fourth-order Cartesian grid-based boundary integral method (BIM) for multiple acoustic scattering problem on closely packed obstacles. We reformulate the exterior Helmholtz value problems (BVPs) as Fredholm equation (BIE) of second kind some unknown density function. Unlike traditional method, distinctive feature our scheme is that do not require quadratures and dire...

High-order Sobolev-type equations are mathematical models used in many applied problems. As is known, cases, it difficult to obtain analytical solutions high-order equations; therefore, they mainly solved by numerical methods. At present, the method of straight lines often solve non-stationary problems physics; this method, discretization first realized only spatial variables, and resulting sys...

A Morley–Wang–Xu (MWX) element method with a simply modified right hand side is proposed for fourth order elliptic singular perturbation problem, in which the discrete bilinear form standard as usual nonconforming finite methods. The sharp error analysis given this MWX method. And Nitsche’s technique applied to MXW achieve optimal convergence rate case of boundary layers. An important feature s...