A Method to Solve Hamilton–Jacobi Type Equation on Unstructured Meshes

A uniform approximation method to solve absolute value equation

In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the ...

On convergence of homotopy analysis method to solve the Schrodinger equation with a power law nonlinearity

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region ...

Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes

In this paper we generalize a new type of limiters based on the weighted essentially nonoscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [31] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the en...