Introductory courses on differential equations cover integration techniques for integrable differential equations. However, most systems of ordinary differential equations are too complicated to be integrated exactly. Therefore, mathematicians have developed ways through which we can approximate such systems. These numerical integrators solve systems of differential equations to within a certai...

This paper analyzes the welfare effects of monopoly differential pricing in the important but largely neglected case where costs of service differ across consumer groups. Cost-based differential pricing is shown to increase total welfare and consumer welfare relative to uniform pricing for broad classes of demand functions, even though total output can still fall or the output allocation betwee...

This paper examines racial and ethnic differences in high cost mortgage lending in seven diverse metropolitan areas from 2004-2007. Even after controlling for credit score and other key risk factors, African-American and Hispanic home buyers are 105 and 78 percent more likely to have high cost mortgages for home purchases. The increased incidence of high cost mortgages is attributable to both s...

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and c...

This paper extends our earlier analysis on approximate linear programming as an approach to approximating the cost-to-go function in a discounted-cost dynamic program [6]. In this paper, we consider the average-cost criterion and a version of approximate linear programming that generates approximations to the optimal average cost and differential cost function. We demonstrate that a naive versi...

In recent years, soft computing methods have generated a large research interest. The synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. A particular evolutionary algorithm (EA) is differential evolution (DE). As for any EA, DE algorithm also requires parameters tuning to achieve desirable performance. In this paper tuning the perturbation factor vector of DE ...