A new multistage Parker-Sochacki method for solving the Troesch’s problem - Akindeinde, Saheed; Adesanya, Samuel; Lebelo, Ramosheuw S.; Moloi, Kholeka C. (International Journal of Engineering and Technology, 2020)
In this article, we introduce a new method to obtain an approximate analytical solution of the highly unstable Troeschâ€™s problem. In the proposed method, without recourse to any hyperbolic tangent transformation or finite term approximation of the hyperbolic sine function, the problem is recast as a system of projectively polynomials which allows straightforward computation of the series solution of the problem. The radius of convergence Â of the series solution to the problem is derived a-priorly in terms of the parameters of the polynomial system. Using a step length ; the problem domain is divided into subintervals, where corresponding subproblems are defined and solved with Parker-Sochacki method with very high accuracy. Highly accurate piecewise continuous approximate solution is thus obtained on the entire integration interval. The obtained solution, which is valid for every choice of the Troesch parameter , showed comparable accuracy to known numerical solutions in the literature. In particular, new results are presented for large values of Â in the range [20;500].