Finding plasma equilibria with magnetic islands
Journal of Computational Physics
Approximation of solutions of singular second-order boundary value problems
SIAM Journal on Mathematical Analysis
On a singular nonlinear elliptic equation
Nonlinear Analysis: Theory, Methods & Applications
Journal of Computational and Applied Mathematics
Analytical-numerical investigation of bubble-type solutions of nonlinear singular problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
For a class of singular free boundary problems with applications in electromagnetism and plasma physics, an analytical-numerical approach is proposed based on the asymptotic expansion of the solution in the neighborhood of the singular points. This approach was already used to approximate the solution of certain classes of singular boundary value problems on bounded (Lima and Morgado (2009) [14]) and unbounded domains (Konyukhova et al. (2008) [12]). Here, one-parameter families of solutions of suitable singular Cauchy problems, describing the behavior of the solution at the singularities, are derived and based on these families numerical methods for the approximation of the solution of the free boundary problems are constructed.