Numerical experience with the integral equation approach to dynamos in finite domains

The integral equation approach to steady dynamos in finite domains is employed to solve the eigenvalue problem for spherically symmetric, isotropic alpha^2 dynamo models. Three examples of the function alpha(r) with steady and oscillatory solutions are considered. A convergence rate proportional to the inverse square of the number of grid points is achieved. Based on this method, a convergence accelerating strategy is developed and the convergence rate is improved dramatically. The computed results show a good agreement with analytical results and results obtained by a differential equation solver. Typically, quite accurate results can be obtained with a few tens of grid points.