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We describe a set of Gaussian Process based approaches that can be used tosolve non-linear Ordinary Differential Equations. We suggest an explicitprobabilistic solver and two implicit methods, one analogous to Picarditeration and the other to gradient matching. All methods have greater accuracythan previously suggested Gaussian Process approaches. We also suggest ageneral approach that can yield error estimates from any standard ODE solver.

On solving Ordinary Differential Equations using Gaussian Processes