GET_LEGENDRE_VALUE_2DER.f90 File Reference

Go to the source code of this file.

Functions/Subroutines
subroutine	get_legendre_value_2der (p2der2, p2, p2der, p1, p1der, n, x)
	Computes Legendre polynomial and its first and second derivative on a given point x.

Function/Subroutine Documentation

get_legendre_value_2der()

subroutine get_legendre_value_2der	(		p2der2,
			p2,
			p2der,
			p1,
			p1der,
			n,
			x
	)

Computes Legendre polynomial and its first and second 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]	p2der2	second 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 32 of file GET_LEGENDRE_VALUE_2DER.f90.

                                             
      implicit real*8 (a-h,o-z)                            
 
      p2=1.d0                                                    
      p2der=0.d0                          
      p2der2=0.d0                          
      if (n.eq.0) return              
      p1=p2
      p2=x
      p1der=p2der
      p2der=1.d0
      p2der2=0.d0
      p1der2=0.d0
      p0der2=0.d0
      if (n.eq.1) return  
      k=1
      p0=p1
      p1=p2
      p0der=p1der
      p1der=p2der
      p0der2 = p1der2
      p1der2 = p2der2
      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
      p2der2=a1*p1der2*x+2.d0*a1*p1der+a2*p0der2
      if (n.eq.2) return  
      do k=2,n-1
        p0=p1
        p1=p2
        p0der=p1der
        p1der=p2der
        p0der2=p1der2
        p1der2=p2der2
        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
        p2der2=a1*p1der2*x+2.d0*a1*p1der+a2*p0der2
      enddo
      return                    

Referenced by phi().

Here is the caller graph for this function: