Dim x( 1) is the root of Double' receiving ercigenway respectively.
1.0 er Method for Finding the Real Root of Quadratic Equation-Tested
Private Subercigenway (A is simple, B is simple and C is simple)' A, B and C correspond to the coefficients of quadratic equation.
Adjust d to double precision.
d = b ^ 2 - 4
If d< is 0.
Msgbox "Δ Δ is less than 0 and has no real root", "Message"
x(0) = 0: x( 1) = 0
Then ElseIf d = 0.
x(0) = -b / (2 * a): x( 1) = x(0)
other
x(0)=(-b-Sgn(b)* Sqr(d))/(2 * a):x( 1)= c/(a * x(0))
If ... it will be over.
End joint
2. 1 findway scan root interval in equal steps-tested
Private sub find way (byval a is single, byval b is single, h is double)' a and b are the endpoints of the interval to be scanned, and h is the step size.
Dim a 1 is double precision.
a 1 = a
do
if f(a 1)* f(a 1+h)& lt； Then = 0
aa = a 1: bb = a 1 + h
outlet connection
If ... it will be over.
a 1 = a 1 + h
Loop while a1< b
If a1> B so
MsgBox "Cannot find the root interval, please try a smaller step size"
outlet connection
If ... it will be over.
End joint
2.2 dichotomy root test
Private function er fenfun (byval a is single, byval b is single, eps is double)' A and b are endpoints of rooted interval, and EPS is error.
Dim x0 is Double, x 1 is Double, x2 is Double, f0 is Double, f 1 is Double, and f2 is Double.
x 1 = a: x2 = b
do
x0 = (x 1 + x2) / 2
f0 = f(x0)
If f0 = 0, then
Exit Do
other
f 1 = f(x 1): f2 = f(x2)
If F0 * f1<; Then 0
x2 = x0
other
x 1 = x0
If ... it will be over.
If ... it will be over.
Abs(x 1-x2) > time cycle; storage battery
x0 = (x 1 + x2) / 2
erfenfun = x0
End function
2.4 Newton Tangent Method-Tested
The private function Newton fxfun (byvalx0 is double, eps is double) is double' x0 is the nearby root, and EPS is the error.
Dim x 1 is of double precision, f0 is of double precision, and f 1 is of double precision.
x 1 = x0
do
x0 = x 1
F0 = f(x0): f 1 = fd(x0) 'fd represents the derivative function of f.
If ABS (f1) < Then eps.
X 1 = x0: exit from Do.
If ... it will be over.
x 1 = x0 - f0 / f 1
Loop until ABS (x1-x0) <; storage battery
newtonfxfun = x 1
End function
2.3 stediedaifun sefensen accelerated iteration method (equation form is x-f(x)= 0)- test.
Private function stediedaifun (byvalx0 as double, eps 1asdouble, eps2asdouble) as double' x0 is the root near the analytical solution, eps 1 is the error of the output result, and eps2 is the criterion for judging whether the iteration can continue.
Dim y is Double, z is Double, and x 1 is Double.
x 1 = x0
do
x0 = x 1
y = f(x0): z = f(y)
If ABS (z-2 * y+x0) < So eps2
MsgBox "In order to satisfy the eps2 condition, the iteration cannot continue"
Exit function
If ... it will be over.
x 1 = x0 - (y - x0) ^ 2 / (z - 2 * y + x0)
Loop until ABS (x1-x0) <; eps 1
stediedaifun = x 1
End function
2.5 Newton tangent method to solve Newton fxnfun n algebraic equation-tested
Newton fxnfun (a () is single, eps is double, and x0 is double) is double 'a () to store the n coefficients of the equation in descending order, EPS is error, and x0 is nearest root.
Dim k is an integer, n is an integer, f0 is a double precision, f 1 is a double precision, and x 1 is a double precision.
N = unbound (a)
x 1 = x0
do
x0 = x 1
f0 = a(0): f 1 = f0
For k = 1 to n-1
f0 = a(k) + f0 * x0
f 1 = f0 + f 1 * x0
Next k
f0 = a(n) + f0 * x0
x 1 = x0 - f0 / f 1
Loop until ABS (x1-x0) <; storage battery
newtonfxfun = x 1
End function
2.6 linecutfun chord cutting method-tested
The private function line cut fun (byval x0 is double, byval x 1 is double, eps is double, n is long) is the limit of iteration times, x0 and x 1 are the endpoints of rooted interval, and EPS is the error.
Mark f0 as Double, f 1 as Double, and f2 as Double.
Dim x2 is Double, and I is Long.
f0 = f(x0): f 1 = f(x 1)
For i = 1 to n
x2 = x 1-(x 1-x0)* f 1/(f 1-F0)
f2 = f(x2)
If ABS (F2) <: Then eps.
Quit for ...
If ... it will be over.
x0 = x 1:x 1 = x2:F0 = f 1:f 1 = F2
Next, I
If i = n+1
MsgBox "The number of calculations required is too low to meet the accuracy requirements"
If ... it will be over.
linecutfun = x2
End function
4. 1 Lagrange interpolation polynomial-tested.
Private function lagrangeczfun (a () is double, byval u is double) is double 'a (1, n) to store n+ 1 nodes, and u is the interpolation point.
Dim i is an integer, j is an integer and n is an integer.
Dim l is Double and v is Double.
v = 0
n = UBound(a，2)
For j = 0 to n
l = 1#
For i = 0 to n
If i = j, go to hulue.
l = l * (u - a(0，i)) / (a(0，j) - a(0，I))
hulue:
Next, I
v = v + l * a( 1，j)
Next J.
Lagrange function = v
End function
4.2 Newton Interpolation-Tested
The private function newtonczfun (a () is double and u is double) stores n+ 1 nodes for double 'a (1, n), and u is the interpolation point.
Dim n is an integer, I is an integer, J is an integer, and K is an integer.
Dim z () is Double, f () is Double, and v is Double.
n = UBound(a，2)
ReDim z(n)，f(n)
For i = 0 to n
z(i) = a( 1，I)
Next, I
For i = 1 to n
k = k + 1
For j = 1 to n
f(j) = (z(j) - z(j - 1)) / (a(0，j) - a(0，j - k))
Next J.
For j = 1 to n
z(j) = f(j)
Next J.
Next, I
f(0) = a( 1，0)
v = 0
For i = n to 0 step-1
v = v * (u - a(0，i)) + f(i)
Next, I
newtonczfun = v
End function
4.3 hermiteczfun Hermite Interpolation Test
The private function Hermiteczfun (a () is double, FD () is double, and U is double) is double 'a (1, n) to store n+ 1 nodes, fd(n) to store the derivative value of n+ 1 nodes, and U is the interpolation point.
Dim l () is Double, ld () is Double, G () is Double, H () is Double, and aim is Double.
Dim n is an integer, I is an integer and j is an integer.
N = unbound (a)
ReDim l(n)，ld(n)，g(n)，h(n)
aim = 0
For i = 0 to n
l(i) = 1: ld(i) = 0
For j = 0 to n
If j = i, then go to hulue.
l(i) = l(i) * (u - a(0，j)) / (a(0，i) - a(0，j))
ld(i) = ld(i) + 1 / (a(0，i) - a(0，j))
hulue:
Next J.
g(i) = ( 1 + 2 * (a(0，i) - u) * ld(i)) * l(i) * l(i)
h(i) = (u - a(0，i)) * l(i) * l(i)
aim = aim + g(i) * a( 1，i) + h(i) * fd(i)
Next, I
hermiteczfun = aim
End function
5.2.1tixingfun variable step integration method-tested
Private function tixingjfff (A is single, b is single, eps is double, and m is long) is double 'A and b are the upper and lower bounds of the integral, EPS is the error, and m is the maximum number of calculations.
Dim h is Double, t 1 is Double, t2 is Double, t is Double, and hh is Double.
Dim n As Long: n = 1
h = b - a: t 1 = h * (f(a) + f(b)) / 2
do
t = 0
For i = 1 to n
t = t + f(a + (i - 0.5) * h)
Next, I
hh = h * t
t2 = (t 1 + hh) / 2
If ABS (T2-t1) <; Eps then exits Do.
t 1 = t2: h = h / 2: n = 2 * n
Circulate until n>2 * meters.
If n>, then 2 * m
MsgBox "The number of calculations is too small to meet the error requirements"
If ... it will be over.
tixingjffun = t2
End function
5.2.2 Simpson Integral Method with Variable Step Size-Tested
Private function simplesonjfun(A is single, b is single, eps is double, and m is long) is double 'A and b are the upper and lower bounds of the integral, EPS is the error, and m is the maximum number of calculations.
Dim n is as long as I am.
Dim h is Double, t 1 is Double, t2 is Double, hh is Double, s 1 is Double, and s2 is Double.
n = 1:h = b-a:t 1 = h *(f(a)+f(b))/2
hh = h *(f((a+b)/2)):s 1 =(t 1+2 * hh)/3
do
n = 2 * n: h = h / 2: t2 = (t 1 + hh) / 2
t = 0
For i = 1 to n
t = t + f(a + (i - 0.5) * h)
Next, I
hh = t * h
s2 = (t 1 + 2 * hh) / 3
If ABS (S2-s1) <; Eps then exits Do.
t 1 = t2: s 1 = s2
Loop until n>m
If n>M Then MsgBox "has too few calculations to meet the error requirements"
simpsonjffun = s2
End function
5.3 Rhomberg integral method
Private function rombergjfun(a is Single, b is Single, eps is Double) is Double.
K is an integer, n is an integer, and h is a double precision.
k = 0: n = 1: h = b - a
End function
First derivative found-tested
Private function ds 1 fun(x0 is single, eps is double) is double' x0, and EPS is error.
Dim h is Double, t 1 is Double, and t2 is Double.
h = 1:t 1 =(f(x0+h)-f(x0-h))/(2 * h)
h = h/2:T2 =(f(x0+h)-f(x0-h))/(2 * h)
Do While Abs(t2-t 1) > battery
t 1 = t2
h = h / 2
t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)
ring
ds 1fun = t2
End function
5.5.2 Second derivative of ds2fun-Tested
Private function ds 2 fun(x0 is single and eps is double) asdouble' x0 is derivative and EPS is error.
Dim h is Double, t 1 is Double, and t2 is Double.
h = 1:t 1 =(f(x0+h)+f(x0-h)-2 * f(x0))/(h * h)
h = h/2:T2 =(f(x0+h)+f(x0-h)-2 * f(x0))/(h * h)
Do While Abs(t2-t 1) > battery
t 1 = t2
h = h / 2
T2 =(f(x0+h)+f(x0-h)-2 * f(x0))/(h * h)
ring
ds2fun = t2
End function