محاسبات عددی

توضيح : تکاليف زير مربوط به درس محاسبات عددی می باشد و با زبان برنامه نويسي GW BASIC حل شده است و فايل برنامه ي هر يک را ميتوان در انتهاي هر تکليف دريافت نمود .

home work 1:

from a difference table for the following data for estimate the degree polynomial needed to produce interpolated .

value corrected to the namber of significante given

write a computer program , then compute the function pat points 3.5 , 7.8 { p(3.5)=? , p(7.8)=? }

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home work 2:

write a simple gauss elimination method to solve a system of in linear equation .

* check program to work properly by a system of equation with known answers.

.21X1+.32X2+.12X3+.31X4=.96

.10X1+.15X2+.24X3+.22X4=.71

.20X1+.29X2+.46X3+.36X4=1.26

.61X1+.90X2+.32X3+.20X4=1.53

X1=X2=X3=X4=1.0    {4 significant: (.9999 to 1.0001)}

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home work 3:

write either

a) a jacobian

b) or a gauss sidel iteration program to solve system of linear equation.

1) in the main program check the form diagonal dominency of the matrix .

if yes , ok

if not , rearrange it to make it did.

150X1+12X2+18X3+30X4=210

70X1+80X2+90X3+300X4=540

40X1+290X2+10X3+50X4=390

35X1+45X2+100X3+20X4=200

X1=X2=X3=X4=1.00                                 ε = .00001

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home work 4:

write a main program with the following subroutines

1) mid - point rule

2) trapezoidal rule

3) simpson's rule

value the integral ∫ (1-x^2)^(3/2) dx,0,1

start with two interval increase the no. of intevals so that you get up to 3 floating point accuracy.

and compare the no. of intervals & solution .

exact = ∫ (1-x^2)^(3/2) dx,0,1= 0.589048622

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home work 5:

write a program to implement

1) Euler's method

2) Rung kutta of order 2 and 4

EX:

to solve dy/dx =3x^3+4x+5+e^(xy)

initial value : y(0) = 0

and find y(2) aecurate to 4 decimalpoints & compare the no of intervals in each case .

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