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It is accepted that given a 2nd order linear or nonlinear ODE au'' + bu' + cu where a, b,c can be functions of x,u,u' with the prime denoting derivative wrt x and that if initial values are prescribed then the solution can be obtained using Runge-Kutta methods etc while if boundary values are prescribed then the ODE could be solved using the Finite Element or Finite difference Method. My question is why can't an Initial value Problem (IVP) be solvable using the Finite Element method?