A novel iterative method for solving the nonlinear Troesch's problem

What is it about?

The method presented in this work is capable of computing the solution, even for extremely high-sensitivity parameter. The method is based on the the Newton–Raphson–Kantorovich approximation method in function space combined with the standard finite difference method. Although, most of the available numerical solvers fail to provide accurate numerical solutions when the sensitivity parameter becomes very large, the method proposed here is able to provide accurate numerical solutions for extremely large values of this sensitivity parameter. Numerical experiments have shown the accuracy of the method compared to existing solvers, as well as its capability to compute the solution for high values of the sensitivity parameter

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Why is it important?

To the best of our knowledge, this is the only available numerical method that is able to compute the solution of Troesch's problem for values of the sensitivity-parameter larger than 100.