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수치해석 2010 년도 봄학기 Homework PowerPoint PPT Presentation


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수치해석 2010 년도 봄학기 Homework. 환경공학과 20080029 김민진. I.1 Taylor 급수를 유도하고 절단 오차를 설명하라. 절단오차 (truncation error) - 수학적으로 엄밀하게 주어지는 함수 f 의 값을 , 유한의 사칙 연산의 반복 계산 식 fa 로 근사하는 경우 , (fa-f) 의 오차가 생김 . - 예를 들면 , 테일러급수를 이용하여 삼각함수를 계산할 때 , 무한급수의 계산을 유한 항까지의 계산으로 중단하기 위해서 , 절단오차가 발생.

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수치해석 2010 년도 봄학기 Homework

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2010 homework

2010 Homework

20080029


I 1 taylor

I.1 Taylor .


2010 homework

  • (truncation error)

    - f , fa , (fa-f) .

    - , , , .


2010 homework

I.2 1) .2) Visual Fortran, Visual C Compiler . 3) Visual Basic .


2010 homework

(1)

  • :: .

  • : 0 .

  • : 1 .

  • : .

  • : . .

  • : .


2010 homework

.


2010 homework

Visual Fortran


2010 homework

Visual C


Iii 1 3 determinant

III.1 3 (Determinant) .( ).


2010 homework

  • A LU A=LU , |A| |A|=|L| |U|

  • . Doolittle LU , L 1, ()

  • . , |A| U . ,LU Pivot , Pivot , m .


2010 homework

  • , |A| U . ,LU Pivot , Pivot , m .

  • Doolittle LU , U Gauss (4.14) . , Gauss Pivot


2010 homework

  • . , Gauss , , Pivot . , .


2010 homework

  • A , .

  • ,I . , (4.4) , . ,LU .


2010 homework

  • X , (5.5) AX=I

  • (5.6) . Doolittle LU A=LU LY=I , UX=Y X . , LY=I 1 , , j 1 n


2010 homework

  • . , , j n 1

    . , Y L , X U , . , LU A , X A . , LU Pivot , X . Pivot .


Iii 2 3 gauss

III.2 3 Gauss .


Iii 3 3 gauss pivot

III.3 3 Gauss Pivot .


Iii 4 3 c fortran

III.4 3 C Fortran .


Iii 5 3 gauss jordan

III.5 3 Gauss-Jordan .


2010 homework

  • ()

  • 1, 1 1 0 . , 1 1/2 .


2010 homework

  • , 2-1, 3-41

  • 2 , 2 1 0 . , 2 -1/3 .


2010 homework

  • , 1-22, 3-(-7)2

  • 3 , 3 1 0 . , 3 -3/56 .


2010 homework

  • , 1-(13/3)3,

  • 2-(-2/3)3

  • , .


Iii 6 4 lu doolittle crout

III.6 4 LU Doolittle Crout .


Iii 7 3 lu excel

III.7 3 LU Excel .


Iii 8 1 jacobi gauss seidel sor excel

III.8 1 Jacobi, Gauss Seidel , SOR , Excel, .


Iv 1 derive the all the algorithms using graphs for the case of bisection secant and newton methods

IV.1 Derive the all the algorithms using graphs for the case of Bisection, Secant, and Newton Methods.


Iv 2 compile and run the given programs by using visual fortran visual basic and visual c compilers

IV.2 Compile and run the given programs by using Visual Fortran, Visual Basic and Visual C Compilers.


Iv 3 solve the example problems by hands using excel program and by the given programs

IV.3 Solve the example problems by hands, using Excel program, and by the given programs.


Iv 4 newton newton raphson

IV.4 Newton Newton-Raphson .


2010 homework

6.2 Newton-Raphson

(1)

(2)

(3)

6.5: 1

(6.5)

(6.6)

Newton-Raphs


2010 homework

  • 6.2.2 Newton-Raphson .

    - Newton-Raphson .

    - (6.5)Newton-Raphson .Newton-Raphson . .

    - (Sol.)

    - 1


2010 homework

- Newton-Raphson

- Newton-Raphson (X)

- = & .

- = .

.


Iv 5 newton

IV.5 Newton . , .


Vii 1 bod arma 1

VII.1 BOD ARMA 1 ( ). .


2010 homework

1)

BOD , BOD . .

, (u) (Q/A).

.

.

x=0 Co x C . .

, .

, Co X=0 .


2010 homework

2)

  • .

    BOD / ln y / x . . , BOD . .

    . Excel Regression() .(r)


Viii 1 sympson

VIII.1 , , Sympson .


2010 homework

,

:

. , .

X=a, X=b, y=f(x) . , [a,b] n , .

, , . , n , 8.1


2010 homework

VIII. 2 , Sympson (, Excel, Program ( ), . , .


Vii 2 arma

VII.2 ARMA .


Viv 2 euler 2 taylor

VIV.2 Euler 2 Taylor .


Viv 3 adams basforth adams moulton

VIV.3 Adams-Basforth Adams-Moulton .


2010 homework

I.1 .


2010 homework

I.2 Fortran Basic Excel Excel . . .


2010 homework

2.4 M1.FOR ( )


2010 homework

  • 2.5 M1.FOR ( )


2010 homework

2.5 M1.FOR ( )


2010 homework

2.6 M1.FOR ( )


2010 homework

2.7 M1-Excel


2010 homework

2.8 M1-Excel


2010 homework

I.3 , .


2010 homework

  • (hyperbolic), (parabolic), (elliptic) .

  • .


2010 homework

  • , . . .


2010 homework

  • . . .


2010 homework

  • , .

  • , .

  • GCA , . . , .


2010 homework

  • . . Excel . BASIC FORTRAN . . Crank-Nicholson (GCN : Generalized Crank-Nicholson Method) (GCA : Generalized Characteristic Averaging Method) .


2010 homework

I.4 GCA , Fortran Basic Excel Excel . . .


2010 homework

  • GCA (Characteristic Method), (Centered Difference (Averaging) Method), (Generalized) Crank Nicholson .

  • 1)

    • .


2010 homework

  • , .

  • , .

  • GCA , . . , .


2010 homework

2) () (Centered Difference (Averaging) Method)

  • . , , .


2010 homework

  • .

  • , , .

  • , ().

  • , .


2010 homework

  • . , , . L(C) .


2010 homework

  • 0 . . .


2010 homework

  • (Weighted Residual Method) , . , , , 0 . Green , , .

  • , ( ) . , (, ) , , , . , (Basis Function) (Shape Function) .


2010 homework

  • , . , , 1 . , , , . Gauss , .


2010 homework

II.

II.1 Green .


2010 homework

  • . .


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II.2 . .


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II.3 .


Ii 4 gauss

II.4 Gauss . ( ).


2010 homework

  • Gauss , 2 . Gauss .


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  • . . . , .


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II.5 .


2010 homework

II.6 , Fortran (m1.for) Excel Excel . . .


2010 homework

  • . . .

  • .


Ii 7 gcn bas gca bas gcn xls gca xls m1 for m1 xls

II.7 (gcn.bas, gca.bas, gcn.xls, gca.xls) (m1.for, m1.xls) ( ).


2010 homework

  • Crank-Nicholson . GCN . , .


2010 homework

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