GET_LEGENDRE_VALUE.f90 File Reference

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Functions/Subroutines
subroutine	get_legendre_value (p2, p2der, p1, p1der, n, x)
	Computes Legendre polynomial and its derivative on a given point x.

Function/Subroutine Documentation

get_legendre_value()

subroutine get_legendre_value	(		p2,
			p2der,
			p1,
			p1der,
			n,
			x
	)

Computes Legendre polynomial and its derivative on a given point x.

Author

Ilario Mazzieri

Date

September, 2013

Version

1.0

Parameters

[in]	n	degree of the polynomial
[in]	x	point
[out]	p2	Legendre polynomial of degree n evaluated in x
[out]	p2der	derivative of p2 evaluated in x
[out]	p1	Legendre polynomial of degree n-1 evaluated in x
[out]	p1der	derivative of p1 evaluated in x

Definition at line 31 of file GET_LEGENDRE_VALUE.f90.

                                                                    
      implicit real*8 (a-h,o-z)                            
      
      p2 = 1.d0                                                    
      p2der = 0.d0                                                    
      if (n .eq. 0) return                                          
      p1 = p2
      p2 = x
      p1der = p2der
      p2der = 1.d0
      if (n .eq. 1) return                               
      do k = 1, n-1
        p0 = p1
        p1 = p2
        p0der = p1der
        p1der = p2der
        dk = dfloat(k)                                         
        a1 = (2.d0*dk+1.d0) / (dk+1.d0)
        a2 = -dk / (dk+1.d0)
        p2 = a1*p1*x + a2*p0
        p2der = a1*p1 + a1*p1der*x + a2*p0der
      enddo
      
      return                    

Referenced by find_root_pol(), make_lgl_nodes(), and make_lgl_nw().

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