Before revision:  The integro-differential formulation  poses challenges to numerical solutions of complicated problems.While various numerical methods based on discretizing the computational domain have been developed and have their own merits,some important issues are yet to be solved , such as the computation of infinite domains, the treatment of softening of boundaries due to an incomplete horizon, and time error accumulation in dynamic processes.
After revision:  The integro-differential formulation poses challenges to numerical solutions of complicated and practical problems. Some important issues attract much attention , such as the computation of infinite domains, the treatment of softening of boundaries due to an incomplete horizon, and time error accumulation in dynamic processes.