A class of variable coefficient elliptic equations solved using BEM

An Accurate Fourier-Spectral Solver for Variable Coefficient Elliptic Equations

We develop a solver for nonseparable, self adjoint elliptic equations with a variable coefficient. If the coefficient is the square of a harmonic function,a transformation of the dependent variable, results in a constant coefficient Poisson equation. A highly accurate, fast, Fourier-spectral algorithm can solve this equation. When the square root of the coefficient is not harmonic, we approxima...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Explicit exact solutions for variable coefficient Broer-Kaup equations

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...

The Tolerant Qualocation Method for Variable-coefficient Elliptic Equations on Curves

The ‘tolerant’ modification of the qualocation method is studied for variable-coefficient elliptic equations on curves. The modification (in which the discrete innerproducts on the righthand side of the qualocation method are replaced by exact integration) allows the same high-order convergence as the standard spline qualocation method but with reduced smoothness assumptions on the exact soluti...