Computation of Troesch Problem by a Modified Newton’s Approach

Abstract

We introduce an improved Newton scheme to solve the nonlinear Troesch problem; which is a nonlinear parameter-sensitive differential equation applied to model plasma confinement in a column.. A predictor-corrector scheme based on a modified backward Euler method was adopted for the Newton’s update. The hyperbolic sine component of the governing equation was converted to its logarithmic analog in order to handle high gradients and discontinuities. This was also found to be useful when the initial position values are not very close to the projected equilibrium. The proposed algorithm is straightforward and offers a relatively high degree of accuracy for a remarkably wide range of values of the sensitivity parameter. The trade-off is a slightly more computation time than the classical Newton’s approach.