NUMERICAL STABILITY; IMPLICIT METHODS
If a numerical method has no restrictions on in order to have y n!0 as n !1, we say the numerical method is A-stable. THE BACKWARD EULER METHOD Expand the function Y(x) as a linear Taylor polynomial about x n+1: Y(x) = Y(x n+1) + (x x n+1)Y0(x n+1) + 1 2 (x x n+1) 2 Y00( n) with n between x and x n+1. Let x = x
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THE SECANT METHOD - University of Iowa
homepage.math.uiowa.eduTHE SECANT METHOD Newton’s method was based on using the line tangent to the curve of y = f(x), with the point of tangency (x 0;f(x 0)).When x 0 ˇ , the graph of the tangent line is approximately the same as the
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homepage.math.uiowa.eduThe differential equations we consider in most of the book are of the form Y′(t) = f(t,Y(t)), where Y(t) is an unknown function that is being sought. The given function f(t,y) of two variables defines the differential equation, and exam ples are given in Chapter 1. This equation is called a first-order differential equation because it ...
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homepage.math.uiowa.eduFor f(x) = log 10 x, with 1 x 0 x x 2 10; this leads to jlog 10 x P 2(x)j h3 9 p 3 max x0 x x2 2log 10 e x3:05572h3 x3 0 For the case of h = :01, we have jlog 10 x P 2(x)j 5:57 10 8 x3 0 5:57 10 8 For comparison, jlog 10 x P 1(x)j 5:43 10 6
A quick example calculating the column space and the ...
homepage.math.uiowa.eduPut A into echelon form and then into reduced echelon form: R 2 –R 1 R 2 R 3 + 2R 1 R 3 R 1 + 5R 2 R 1 R 2 /2 R 2 R 1 + 8R 3 ...
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