CME263H1 Lecture Notes - Lecture 39: Heat Equation
23 Nov 2020
School
Department
Course
Professor
1
Predictor Yui eYu th fXn yn
Corrector Yun EYu th tftxn Yn Jtf Xm
Ya
if
fck y
tXun YEI I
wl
l
t
gXu Xu
11
ifun 4T
tf XuthyEa
local error iorder htruncation error
Global error order hltotal error
2ndorder method
Two function evaluation at eachstep
EX y2XY YU
Solution ye 1
over afixed interval of X
Tthe number of steps
Ijlis proportional to Yu
Xi 141 Xj x
Total error truncation error Xnumber of steps
htheh
The total error in the Euler method is proportional to h
First order method
In addition to the total error from numerical method there
exists round off error y
Yo Itemization
Document Summary
Predictor yui e yu th f xn yn. Yun e yu th t ft xn yn jtf xm fck y. Xu i g fun 4 tf xuthyea t l lt. T local error i order h truncation error. Solution ye over a fixed interval of x. Xi the number of steps is proportional to yu x. Total error truncation error x number of steps h theh. The total error in the euler method is proportional to h. In addition to the total error from numerical method there exists round off error. Yue i yu t kk tf kit rok if o. Method e aeiei 9 1 theft hah has. Yue ynthf xun yun when y e flky is linear the method does not require iteration yhtl flxn i. yntilyhtl flxnn. int. P. de an equation that contains one or more partial derivatives of an unknown function that depends on independent variables at leasttwo i one d wave equetion one d heat equation.
