The regularity of the right-hand side function exactly classifies the computational and logical difficulty of solving the ODE initial value problem, corresponding to each level of the Big Five hierarchy from polynomial-time solvability to transfinite computation.
An effective cauchy-peano existence theorem for unique so- lutions.International Journal of Foundations of Computer Science, 7(2):151– 160
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Relating the Computational and Logical Difficulty of Solving ODEs: From Polynomial to Discontinuous Right-Hand Sides
The regularity of the right-hand side function exactly classifies the computational and logical difficulty of solving the ODE initial value problem, corresponding to each level of the Big Five hierarchy from polynomial-time solvability to transfinite computation.