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Solving nonlinear ODE with ODE45 fails at bifurcation point?

  1. Aug 15, 2011 #1
    Hello everybody,

    Background and problem description

    I have derived an analytical expression for an implicit frequency response function. To verify it, I would like to check with a numerical solution. For very weak nonlinearities, congruence is obtained. For weak nonlinearities, the numerical solution cannot follow the solution curve (a hysteresis curve). It seems very much like the solution curve jumps at the lower bifurcation point. I have attached a screenshot of a graph generated in Matlab showing how the numerical solution behaves alongside the analytical solution.

    Attempts to solve the problem

    I have tried to integrate from both [0 n] (where n is an arbitrary time constant) and from [-n 0]. I have also tried to change the ODE solver [ODE45, ODE23s, ODE23t, ODE23tb and ODE15s (in case the problem is stiff)]. I update the initial guess provided to the ODE-solver for each iteration. Changing the tolerances when using the different ODE solvers has not provided any different results. I have considered implementing other approaches such as the tangent method and/or the pseudo-arclength continuation method. But I am not sure whether these approaches will solve my problem.

    Any help/inspiration/ideas/thoughts/tricks/... would be highly appreciated!

    Kind regards,
    Jason
     

    Attached Files:

    • ODE.jpg
      ODE.jpg
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  2. jcsd
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