A semilinear elliptic equation dΔu - u + up = 0 over the unit ball in ℝ2 with positive solution and the homogeneous Neumann boundary condition is considered. This equation models applications like chemotactic aggregation and biological pattern formation. Focusing on solving the discretized version of the equation, this work proposes an efficient algorithm that combines a newly developed discretization scheme on polar coordinates with a fast Fourier solver. An analysis of the induced matrix structures proves the algorithm converges to positive solutions; the analysis also establishes the q-axial symmetry and monotonicity behavior of the solutions. Numerical experiments were conducted to visualize various solution forms that are new to the best of our knowledge. The experiments also illustrated sensitivity behavior of the solutions.
|頁（從 - 到）||261-279|
|期刊||Numerical Methods for Partial Differential Equations|
|出版狀態||已發佈 - 2002 五月|
ASJC Scopus subject areas