A_04 GUASSIAN QUADRATURE METHOD FOR 3(I) AND 3(II), Fortran

A_04 GUASSIAN QUADRATURE METHOD FOR 3(I) AND 3(II)

Program Guassian_Quadrature_method
Call GQSI(3)
Call GQSI(4)
Call GQDI(3,4)
Call GQDI(4,3)
End Program

Subroutine GQSI(n)
Implicit None
Real::c(4),t(4),f,s
Integer::i,j
Integer,intent(in)::n
If (n==4)then
 c(1) = 0.3478548451
 c(2) = 0.6521451549
 c(3) = c(2)
 c(4) = c(1)
 t(1) = 0.8611363116
 t(2) = 0.3399810436
 t(3) = -1.0 * t(2)
 t(4) = -1.0 * t(1)
 elseif(n==3)then
 c(1) = 0.5555555556
 c(2) = 0.8888888889
 c(3) = c(1)
 t(1) = 0.7745966692
 t(2) = 0
 t(3) = -1.0 * t(1)
 end if
 s=0
 Do i=1,n
 s = s+ c(i)*F(t(i))
End Do
Write(*,'(5x,A,I1,A,F20.18)')"The value of single integration  for n=",n," : ",s
End Subroutine

Subroutine GQDI(n,m)
 Implicit None
Real::cn(4),tn(4),cm(4),tm(4),f,s,h1,h2,k1&
&,k2,a,b,c1,d1,sx,x,y,fxy
 Integer::i,j
 Integer,intent(in)::n,m
 if (n==4)then
 cn(1) = 0.3478548451
 cn(2) = 0.6521451549
 cn(3) = cn(2)
 cn(4) = cn(1)
 tn(1) = 0.8611363116
 tn(2) = 0.3399810436
 tn(3) = -1.0 * tn(2)
 tn(4) = -1.0 * tn(1)
 elseif(n==3)then
 cn(1) = 0.5555555556
 cn(2) = 0.8888888889
 cn(3) = cn(1)
 tn(1) = 0.7745966692
 tn(2) = 0
 tn(3) = -1.0 * tn(1)
 end if
 if (m==4)then
 cm(1) = 0.3478548451
 cm(2) = 0.6521451549
cm(3) = cm(2)
 cm(4) = cm(1)
 tm(1) = 0.8611363116
 tm(2) = 0.3399810436
 tm(3) = -1.0 * tm(2)
 tm(4) = -1.0 * tm(1)
 elseif(m==3)then
 cm(1) = 0.5555555556
 cm(2) = 0.8888888889
 cm(3) = cm(1)
 tm(1) = 0.7745966692
 tm(2) = 0
 tm(3) = -1.0 * tm(1)
 end if
 a=1.4
 b=2.0
 c1 = 1.0
 d1 = 1.5
 h1=(b-a)/2
 h2 = (b+a)/2
 s=0
 Do i = 1,m
 sx =0
 x = h1*tm(i) + h2
 k1 = (d1- c1)/2.0
 k2 = (d1+c1)/2.0
 Do j=1,n
 y = k1*tn(j)+k2
 sx = sx + cn(j) * fxy(x,y)
 End Do
s = s + cm(i)*k1*sx
 End Do
 s = s*h1
 Write(*,'(5x,A,I1,A,I1,A,F20.18)')"The value of double integration for n=",n,", m= ",m," : ",s
End Subroutine

Function f(t)
Implicit None
Real::t,f
 f = 0.5*(((1.0+t)/2.0)**2.)*exp((1.0+t)/2.0)
End Function

Function fxy(x,y)
Implicit None
Real::x,fxy,y
 fxy = Log(x+2.0*y)
End function


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