A Novel Approach to the Initial Value Problem with a complete validated algorithm

Bingwei Zhang, Chee Yap

We consider the first order autonomous differential equation (ODE) ${\mathbf{x}}^{\prime }=\mathbf{f}(\mathbf{x})$ where $\mathbf{f}:{\mathbb{R}}^n\to {\mathbb{R}}^n$ is locally Lipschitz. For ${\bf x}_0\i…