MATH 411 Numerical Methods BYU

COMPUTATIONAL PHYSICS 430 PARTIAL DIFFERENTIAL EQUATIONS Ross L. Spencer and Michael Ware Department of Physics and Astronomy Brigham Young University COMPUTATIONAL PHYSICS 430 PARTIAL DIFFERENTIAL EQUATIONS Ross L. Spencer and Michael Ware N263 ES

Math 411: Optimization Newtons Method xn+1 = xn Df (xn )1 f (xn ). Instead of actually computing the inverse, we solve the equation for yn Df (xn )yn = f (xn ). Then set xn+1 = xn + yn . Broydens Method Initialize with A0 = Df (x0 ) Set x1 = x0 A1

Denition 1. A function f (x) is said to interpolate the set of points {(xj , yj )}n if f (xj ) = yj , for all j = 0, . . . , n. j=0 1. Polynomial Interpolation Theorem 2. Given the set {(xj , yj )}n , where each xj is distinct, j=0 there exists a uni

Boundary-Value Problems Finite Dierences Consider the boundary-value problem p(x)y (x) + q(x)y (x) + r(x)y(x) = f (t), where y(a) = and y(b) = . We discretize the domain into n + 1 evenly-spaced points {xj }n , where j=0 x0 = a and xn = b. Let yj =

Math 411: Numerical Methods Winter Term 2009 Professor: Vianey Villamizar Office: 366 TMCB Class: 9:00 - 9:50 a.m. MWF 1020 JKB Email/Phone: vianey@math.byu.edu / 422-1754 Web page: www.math.byu.edu/~vianey Office Hours: Monday 4:00 - 5:30 p.m. (at m

PROOF THAT THE FUNCTIONAL ITERATION CONVERGES TO p.

MATHEMATICS 411-1 WINTER SEMESTER 2002 Classroom: Class Time: Instructor: Oce Hours: Text: Grading: 123 HRCB. 9:009:50 MWF. John Dallon, 312 TMCB, 378-1205, dallon@math.byu.edu. Tentatively 10:0010:50 p.m. MF and other times by appointment. Numeric

MATH 411 Project 1 1. The Kermack-McKendrick model for the course of an epidemic in a population is given by the system of ODEs y1 = -cy1 y2 , y2 = cy1 y2 - dy2 , y3 = dy2 , (1) (2) (3) where y1 represents susceptibles, y2 represents infective in

MATH 511 Chapter 1 0.1 0.1.1 Derivation of Finite Dierence (FD) Approximations Centered Dierence for u (x) A second order nite dierence approximation for u (x) at x = x is given by D0 u() = x 1 [u( + h) u( h)] x x 2h h2 u (). x 6 (1) with an