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...

Efficient solution techniques for high-order accurate time-dependent problems are investigated for solving the two-dimensional non-linear Euler equations in this work. The spatial discretization consists of a high-order accurate Discontinuous Galerkin (DG) approach. Implicit time-integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods. ...

Newton’s iteration method is widely used in numerical methods, but its convergence low. Though a higher order algorithm leads to fast convergence, it always complex. An optimal formulation much needed for both and simple calculation. Here, we develop two-step fourth-order iterative based on linear combination of two schemes nonlinear equations, explore the criteria proposed also demonstrate val...