Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems

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Multi-scale computation methods: Their applications in lithium-ion battery research and development (2016, methodology): “[152] This ﬁnite difference method is also widely used in LIB simulations.”
Weak Adversarial Networks for High-dimensional Partial Differential Equations (2019, methodology): “This problem is considered very challenging for the classical numerical methods, such as the finite difference method [32], which can be unstable for problems defined on nonconvex domains.”
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks (2019, methodology): “In this regime, explicit methods are fundamentally unstable for hyperbolic PDEs thus one must resort to costly implicit methods which require expensive matrix inversions [26, 34].”