Teorema:
Sea d_{x}[y(x)] = y+x+(k+(-1)) ==>
[Ej][ (1/h)·( y_{n+1}+(-1)·y_{n} ) = y_{n}+j ] es un método numérico convergente a y(x)
Demostración:
Sea h = 0a & j = (-1)·((k/a)+1) ==>
y_{n+1} = y_{n}+h·( y_{n}+j ) = y_{n}·(1+h)+hj
y_{n+1} = y_{0}·(1+h)^{n}+nhj
Sea y_{0} = 1 ==>
y(a) = y_{oo} = e^{a}+(-k)+(-a)
Teorema:
Sea d_{x}[y(x)] = y+x^{2}+(k+(-2)) ==>
[Ej][ (1/h)·( y_{n+1}+(-1)·y_{n} ) = y_{n}+j ] es un método numérico convergente a y(x)
Demostración:
Sea h = 0a & j = (-1)·((k/a)+2+a) ==>
y_{n+1} = y_{n}+h·( y_{n}+j ) = y_{n}·(1+h)+hj
y_{n+1} = y_{0}·(1+h)^{n}+nhj
Sea y_{0} = 1 ==>
y(a) = y_{oo} = e^{a}+(-k)+(-1)·2a+(-1)·a^{2}
Teorema: [ de sp-line cuadrática ]
P(x) = (x+(-1)·x_{j})·(x+(-1)·x_{k})·( (x_{i}+(-1)·x_{j})·(x_{i}+(-1)·x_{k}) )^{(-1)}·f(x_{i})
Teorema: [ de sp-line cúbica ]
Q(x) = ...
... (x+(-1)·x_{j})·x·(x+(-1)·x_{k})·( (x_{i}+(-1)·x_{j})·x_{i}·(x_{i}+(-1)·x_{k}) )^{(-1)}·f(x_{i})
Teorema:
Sea d_{x}[y(x)] = y^{m} ==>
[Ej][ (1/h)·( y_{n+1}+(-1)·(y_{n})^{j} ) = ( y_{n} )^{m} ] es un método numérico convergente a y(x)
Demostración:
Sea h = 0 & j = ( 1/(1+(-m))^{0} ) ==>
y_{n+1} = (y_{n})^{j}+h·(y_{n})^{m} = (y_{n})^{m+[j+(-m):h]}
y_{n+1} = (y_{0})^{( 1/(1+(-m)) )^{0n}}
Sea y_{0} = a ==>
y(a) = y_{oo} = a^{( 1/(1+(-m)) )}
Teorema:
Sea f_{n}(x): ( x+(-a) )^{n} ---> ( x+(-a) )^{n+1} ==>
[Ex][ f_{n}(x) está compactificada en 2 clases ]
Teorema:
Sea f_{n}(x): ( e^{x}+(-a) )^{n} ---> ( e^{x}+(-a) )^{n+1} ==>
[Ex][ f_{n}(x) está compactificada en 2 clases ]
Teorema:
Sea f_{n}(P(x)): d_{x...x}^{n}[P(x)]·h(x) ---> Q(x) [o(x)o] ( x /o(x)o/ H(x) ) ==>
[EP(x)][ f_{n}(P(x)) está compactificada en 2 clases ]
Demostración:
d_{x}[ sinh(x) [o(x)o] ( x /o(x)o/ H(x) ) ]·h(x) = cosh(x)
d_{x}[ cosh(x) [o(x)o] ( x /o(x)o/ H(x) ) ]·h(x) = sinh(x)
