Abstract
It is an important issue to numerically solve the time fractional Kardar–Parisi–Zhang equation on unbounded domains, which is a universal model to study the dynamics of the interface with memory effects. The artificial boundary method is adopted to circumvent the problems defined on unbounded domain and retain the same dynamics as the original problem on a bounded domain. The artificial boundary conditions are designed by combining the ideas of operator splitting approach and artificial boundary method to overcome the unboundedness of the physical domain, nonlocality and nonlinearity of the time fractional Kardar–Parisi–Zhang equation. The bounded and convergent properties are analyzed rigorously. The accuracy and feasibility of the proposed method are verified by numerical results.
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