A numerical method for solving a class of fractional optimal control problems (FOCPs) is presented. First, the FOCP is transformed into an equivalent variational problem, then using Lagrange polynomials, the problem is reduced to the problem of solving a system of algebraic equations. With the...

As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to...

Solving economic models with heterogenous agents requires computing aggregate dynamics consistent with individual behaviors. This paper introduces the ?nite volume method from the mathe-matics literature to enlarge the set of numerical methods available to compute dynamics in continuous time....

Introduction -- The Neoclassical GrowthModel Under a Constant Savings Rate -- Optimal Growth: Continuous Time Analysis -- Optimal Growth: Discrete Time Analysis -- Numerical Solution Methods -- Endogenous Growth Models -- Additional Endogenous Growth Models -- Growth in Monetary Economies:...

Cover -- Title Page -- Copyright -- Contents -- Preface -- Who Should Read this Book? -- PART A Mathematical Foundation for One‐Factor Problems -- CHAPTER 1 Real Analysis Foundations for this Book -- 1.1 Introduction and Objectives -- 1.2 Continuous Functions -- 1.2.1 Formal Definition of...

The problem of periodic flow of an incompressible fluid through a pipe, which is driven by an oscillating pressure gradient (. a reciprocating piston), is investigated in the case of a large Reynolds number. This process is described by a singularly perturbed parabolic equation with a periodic...

The numerical analysis for the systems governed by distributed models of Hopfield-type neural networks is studied. When the state space is of dimensional one, a new scheme of numerical solutions based on finite element method (FEM) is constructed, in which the Gauss-Legendre quadrature of...