B-Spline Solution and the Chaotic Dynamics of Troesch's Problem

A B-spline method is presented for solving the Troesch problem. The numerical approximations to the solution are calculated and then their behavior is studied and commenced. The chaotic dynamics exhibited by the solutions of Troesch's problem as they were derived by the decomposition method approximation are examined and an approximate critical value for the parameter λ is introduced also in this study. For the parameter value slightly less than λ ≈ 2.2, the solutions begin to show successive bifurcations, nally entering chaotic regimes at higher λ values. The e ectiveness and accuracy of the B-spline method is veri ed for di erent values of the parameter, below its critical value, where the rst bifurcation occurs.

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