We introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly.

This paper presents a mathematical model to solve the vehicle routing problem with soft time windows (VRPSTW) and distribution of products with multiple categories. In addition, we include multiple compartments and trips. Each compartment is dedicated to a single type of product. Each vehicle is allowed to have more than one trip, as long as it corresponds to the maximum distance allowed in a workday. Numerical results show the effectiveness of our model.

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