Precise and realistic numerical modeling of seismic wave and rupture propagation has become essential for investigating earthquake physics and Earth's structure. In this work, we present an accurate 2D numerical method for in-plane rupture propagation in elastic media that considers laboratory-derived constitutive friction laws (rate- and state-dependent). Accurate description of the complex dynamics along the rupture path is achieved by a combination of representing the fault surface with split-nodes to accommodate discontinuities in tangential velocity, and a high-order discretization of the whole model (elastodynamics and faulting boundary conditions). Mimetic finite differences are used for spatial differentiation. Convergence and accuracy result comparable to a highly-precise boundary integral method, when errors of on-fault fields (tractions, slip velocities, and one state variable) are quantified.