Today, better numerical approximations are required for multi-dimensional SDEs to improve on the poor performance of the standard Monte Carlo integration. With this aim in mind, the material in the thesis is divided into two main categories, stochastic calculus and mathematical finance. In the former, we introduce a new scheme or discrete time approximation based on an idea of Paul Malliavin wh...

according to interactions in multiple grade classes, the present study aims to compare different class compositions in three different groups of fourth-grade multiple grade students in implicit learning and academic achievement. statistical population consists of all fourth grade public elementary school students in piranshahr. 3 groups of students including 8 girls and 8 boys were randomly sel...

and Applied Analysis 3 Now we give the definition of local and global errors. Definition 1. Let x(t) denote the exact solution of (1). The local approximate solution x̃(t k+1 ) starting from x(t k ) by SSTM (2) given by x̃ (t k+1 ) := x (t k ) + Λ (x (t k ) , ?̃? (t k ) , h, ΔW k ) , (9) where ?̃?(t k ) denotes the evaluation of (3) using the exact solution, yields the difference δ k+1 := x (t k+1 ...

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

We thank Gilles Duranton, Harold Elder, William Fischel, Joe Gyourko, Caroline Hoxby, Bob Inman, Loretta Mester, Wallace Oates, Todd Sinai, William Strange and seminar participants at the ASSA meetings, the NBER meetings, the Public Choice meetings, the Wharton School, and Federal Reserve Bank of Philadelphia for helpful comments. We also thank the Wharton GIS Lab and Susan Wachter and Paul Amo...

in this paper an efficient dual time implicit approach is used to solve viscous laminar flow around two bodies with general motion. therefore, the grid includes a background grid and two sets of grids around the moving bodies. rotational and translational motions of two bodies are managed separately in this grid arrangement. in this work the overset concept for hybrid grid is used and flow vari...

We study the complexity of approximating stochastic integrals with error ε for various classes of functions. For Ito integration, we show that the complexity is of order ε−1, even for classes of very smooth functions. The lower bound is obtained by showing that Ito integration is not easier than Lebesgue integration in the average case setting with the Wiener measure. The upper bound is obtaine...

INCREMENT INTERFACE Increment; ATTRIBUTES Errors:SET OF ERRORS; expanded:BOOLEAN; father: Increment; doc_ver: DocumentVersion; END ATTRIBUTES; END ABSTRACT INCREMENT INTERFACE Increment. TERMINAL INCREMENT INTERFACE ClassIdentifier; INHERIT Increment; REGULAR EXPRESSION {[A−Za−z][A−Za−z0−9_]*} END REGULAR EXPRESSION; SEMANTIC RELATIONSHIPS IMPLICIT Constructors:SET OF Constructor.Constructs; IM...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical result...