We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation which the solutions can be obtained in fixed number forward backward alternating substitutions. The use novel combination implicit explicit time discretizations one-dimensional case Strang splitting method several dimensional case. are described equati...

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first...

In the current research work, fractional version of logistic differential model is studied with Allee effect which includes a threshold population. It also initial conditions. The definition derivative utilised in this Caputo-Fabrizio. order to give solution posed problem by an implicit representation, method based on properties used.

An efficient and robust implicit operator for the point Gauss–Seidel method is presented for solving the compressible Euler equations. The new implicit operator was derived by adding a scalar form of artificial dissipation to the upwind implicit side. The amount of artificial dissipation was locally adjusted using a weighting factor based on the solution gradient. For validation, the performanc...

Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...