Segmented Regression and Difference-in-Difference Methods

Alternating difference block methods and their difference graphs

The general concept of a class of alternating difference block methods and their difference graphs are introduced. The methods are unconditionally stable, and according to the difference graphs the design of parallel algorithms and programs of the methods are flexible and easy. The traditional alternating explicit-implicit method, the AD1 method, the AGE method, the Block AD1 method and the ABE...

Composite Mesh Difference Methods

Finite Difference Methods

In this notes, we summarize numerical methods for solving Stokes equations on rectangular grid, and solve it by multigrid vcycle method with distributive Gauss-Seidel relaxation as smoothing. The numerical methods we concerned are MAC scheme, nonconforming rotate bilinear FEM and nonconforming rotate bilinear FVM. 1. PROBLEM STATEMENT We consider Stokes equation (1.1) 8 >< >: μ ~ u +rp =~ f in ...

Finite Difference Methods

1 STATEMENT OF THE PROBLEM Our goal is to introduce how derivatives can be approximated by using difference quotients. Suppose we have an interval [a,b] ⊂ R. Let a = x0 < x1 < ·· · < xN−1 < xN = b be a partition. We call {x1, . . . , xN−1} the interior points, and {x0, xN } the boundary. Given a function f : [a,b] → R, we want to approximate the derivative f ′ using our partition. 2 DIFFERENCE ...

Multiplicative Finite Difference Methods

Based on multiplicative calculus, the finite difference schemes for the numerical solution of multiplicative differential equations and Volterra differential equations are presented. Sample problems were solved using these new approaches.