Explicit and Implicit Methods In Solving Differential Equations

Differential equations are equations that involve an unknown function and derivatives. Euler's method are efficient methods to yield fairly accurate approximations of the actual solutions. By manipulating such methods, one can find ways to provide good approximations compared to the exact solution of parabolic partial differential equations and nonlinear parabolic differential equations.

Efficiency and Continuity in Public Finance: The Ottoman System of Taxation

Economic historians have recently emphasized the importance of integrating economic and historical approaches in studying institutions. The literature on the Ottoman system of taxation, however, has continued to adopt a primarily historical approach, using ad hoc categories of classification and explaining the system through its continuities with the historical precedent. This paper integrates economic and historical approaches to examine the structure, efficiency, and regional diversity of the tax system. The structure of the system made it possible for the Ottomans to economize on the transaction cost of measuring the tax base. Regional variations resulted from both efficient adaptations and institutional rigidities.