Function ( ' tau ' , real = True , positive = True ) ( s ) ,
Function ( ' kappa ' , real = True ) ( s ) ,
Function ( 'N ' , real = True , positive = True ) ( s ) ,
Function ( 'b ' , real = True , positive = True ) ( s ) ,
, On définit les séries formelles, quand h tend vers 0, associées à (1 + ??(s)h n(s,?h 2 ) n(s,?h 2 ) noté nxi
Function ( ' n0 ' , real = True , positive = True ) ,
, +3) //2+2) : 29 n . append (( -1) ** q * n [0]*( sy . factorial ( q ) * k ** q -eta [ q ]( s ) ) ) nbTerm +3) : 37 dxn += n, eta = sy . symbols ( ' eta0 : '+ str ( nbTerm +3) , cls = sy . Function , real = True ) 26 in range
, La matrice ME et les fonctions FtoVExp et VtoFExp permettent de résoudre l'équation différentielle en ? à s fixé ?? ?? ? + 4b(s)? ? ? = S dans R ne
, La solution est ? = VtoFExp(ME * FtoVExp(S))
,
,
vec = sy . zeros ( NE ,1) 56 for j in range ( NE ) : 57 vec [j ,0] = fct . coeff (r , j ) in range ( NE ) : 63 fct += vec, p.55 ,
,
, NA = 2*( na +1)
zeros ( NA , NA ) ,
, MTA [2* j -3 ,2* j +1] = -j *( j -1)
, , vol.1
, vec = sy . zeros ( NA -1 ,1), p.81
, * z * t ) ) in range ( na +1) : 85 vec [2* j ,0] = fctAi . coeff (z , j ) 86 for j in range ( na ) : 87 vec [2* j +1 ,0] = fctAp . coeff (z , j ) in range ( na ) : 93 fct += vec
, Les définitions des fonctions pour dériver par rapport à s, ? et ? les fonctions ?(s, ?) exp (im?(s)) et ?(s, ?) exp (im?(s))
, ph : h **3* expr . diff ( s ) +2* sy . I * ph * expr 98 dzPhi = lambda expr : h * expr, p.99
, ph : h **3* expr . diff ( s ) +2* sy . I * ph * expr -h **3*2* r * b . diff ( s ) * expr
, drPsi = lambda expr : expr . diff ( r ) -2* b * expr Les premiers termes de l'asymptotique
,
degree ( sy . Poly ( edPsi . coeff (h , q ) ,r ) , gen = r ) ) ,
, Différentes vérifications que les termes de l'asymptotique on bien étaient calculé
, # Check 167 print
, dap = " + str ( dap ) + " <= " + str ( na -1) ) ( ", p.-
, Verification a nbTerm " + str ( nbTerm ) )
, nbTerm +3) ) ) . expand (
, nbTerm +3) ) ) . expand (
, nbTerm +1) ) ) . expand (
, nbTerm +1) ) ) . expand () . removeO (, p.180
, Equation differentielle sur psi , O ( h^" + str ( nbTerm +1) + " ) " )
, Equation differentielle sur phi , O ( h^" + str ( nbTerm +3) + " ) " )
, Equation saut fonctions , O ( h^" + str ( nbTerm +1) + " ) " )
, saut0 += ( psi . subs (r ,0) -phi . subs (z ,0) . subs
, Equation saut derivees , O ( h^" + str ( nbTerm +1) + " ) " )
, saut1 += ( psir . subs (r ,0) -N * phiz . subs (z ,0) . subs, p.-
1. Ce script peut-être simplifié et ainsi accéléré dans les trois cas suivants : le cas générale 2D avec un indice constant ,
URL : https://hal.archives-ouvertes.fr/pasteur-01256155
, le cas radial 1D avec un indice variable
, le cas radial 1D avec un indice constant
,
symbols ( 'x ' , real = True ) # x = tau * sigma 13 h , n0 , t = sy . symbols ,
, Hermite et on peut exprimer ? j (x) et x ? j (x) en fonction de ? j?1 et ? j+1 . La liste D défini comment remplacer ? j (x) et la liste X défini comment remplacer x ? j (x). La liste solveOH défini comment résoudre l
, diff ( x ) , sy . sqrt ( sy . Rational (i ,2) ) * GH [i -1]( x ) 15 -sy . sqrt ( sy . Rational ( i +1 ,2) ) * GH [ i +1]( x ) ) for i in range
, Rational ( nb -1 ,2) ) * GH
, ( x ) , sy . sqrt ( sy . Rational (i ,2) ) * GH, p.20
, Rational ( i +1 ,2) ) * GH [ i +1]( x ) ) for i in range
,
, ) ** q * n0 *( sy . factorial ( q ) -eta [q -3]) ) in range (1 , nbTerm +3) : 47 n10 += n [ q ]*( x * h / t ) ** q /( n0 * sy . factorial ( q ) ) in range, nbTerm +3) : 55 ina +=
, nbTerm +3) ) ) . expand () . removeO (
, ( x ) , sy . sqrt ( sy . Rational (i ,2) ) * GH
, Rational ( i +1 ,2) ) * GH [ i +1]( x ) ) for i in range
, Rational ( nb ,2) ) * GH, x ) ) ) ( ", p.-
, Equation differentielle sur phi , O ( h^" + str ( nbTerm +3) + " ) " ) ( ", p.-
, ne = nbTerm 9 nb = 2* j +1+3* nbTerm +1
symbols ( ' f0 : '+ str ( nb +1) , cls = sy . Function , real = True, p.11 ,
,
symbols ( 'x rho ' , real = True ) # x = tau * sigma 14 h , n0, p.15 ,
,
,
, vec = sy . zeros ( NE ,1) 26 for i in range ( NE ) : 27 vec, p.25
,
, ) ** q * n0 *( sy . factorial ( q ) -eta [q -3]) ) in range, nbTerm +3) : 96 n10 += n [ q ]*( x * h / t ) ** q /( n0 * sy . factorial ( q ) ) in range (1 , nbTerm +3) : 104 ina +=
, n20 = ((1+ n10 ) **2+ sy . O ( h **( nbTerm +3) ) ) . expand () . removeO (
, Equation differentielle sur psi , O ( h^" + str ( nbTerm +1) + " ) " )
, Equation differentielle sur phi , O ( h^" + str ( nbTerm +3) + " ) " )
, Equation saut fonctions , O ( h^" + str ( nbTerm +1) + " ) " )
, Equation saut derivees , O ( h^" + str ( nbTerm +1) + " ) " )
, saut1 += (( ps1 -b * psi ) . subs (r ,0) -h * N * phi . subs ( trace1 ) ) . expand (, p.-
,
,
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