This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with multiple time scales. These treat different partitions the system timesteps a more targeted and efficient solution compared to monolithic single rate approaches. With implicit used across all partitions, must find balanc...

Social relationship and business connections create implicit benefits between borrowers lenders. We model how repayment enforcement costs influence credit allocation, cost, renegotiation. The optimal solution illustrates that financing with may achieve lower costs, higher managerial effort, better outcomes for both This result is consistent the continuing expansion of alternative despite formal...