In this study, we present a classification method for ternary small data using the modified Allen–Cahn (tAC) system. The governing system is tAC equation with fidelity term, which keeps solution as close possible to given data. To solve apply an operator splitting method. We use implicit-explicit finite difference solving split equations. validate robust and superior performance of proposed num...

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differe...

We establish forward and backward relations between entropy satisfying BGK relaxation models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for general systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the conv...

In the current study we investigate the two-stage iterative method for solving linear systems. Our new results shows which splitting generates convergence fast in iterative methods. Finally, we solve the Poisson-Block tridiagonal matrix from Poisson's equation which arises in mechanical engineering and theoretical physics. Numerical computations are presented based on a particular linear system...

We study the resurgent structure associated with a Hamilton Jacobi equation This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching We derive the Bridge equation which encompasses in nitely many resurgent relations satis ed by the formal solution and the other components of the formal integral