richardson nell
DESCRIPTION
calculosTRANSCRIPT
EJEMPLO 1: Calcular la derivada en x = 0.5 por Richardson
x f(x)0.1 0.095310180.3 0.2623642640.4 0.336472237 Valor "verdadero"0.5 0.405465108 f'(0.5) = 0.6666666666670.6 0.4700036290.7 0.5306282510.9 0.641853886
h k = 0 k = 1 k = 20.8 0.6831796330.4 0.670659966 0.6664867443290.2 0.667656963 0.666655962001 0.666667243179
EJEMPLO 2: Extrapolar el valor en cero a partir de los valores tabulados
h f(h)0.1 2.728286841459
0.05 2.7195319066090.025 2.718438079680
0.0125 2.718301359728
TABLA DE DIFERENCIAS
h f(h) Delta Delta^2 Delta^3h0 0.1 2.728286841459h1 0.05 2.719531906609 -0.008755h2 0.025 2.718438079680 -0.001094 0.007661h3 0.0125 2.718301359728 -0.000137 0.000957 -0.006704
Hipótesis: f(h) = a + b h^3 + c h^6 + d h^9
EXTRAPOLACIÓN DE RICHARDSON D_j^(k) = D_{j+1}^(k-1) + (D_{j+1}^(k-1)-D_j^(k-1))/(8^k-1))
h k = 0 k = 1 k = 2 k = 3j = 0 0.1 2.728286841459j = 1 0.05 2.719531906609 2.718281201631j = 2 0.025 2.718438079680 2.718281818690 2.718281828484j = 3 0.0125 2.718301359728 2.718281828306 2.718281828459 2.718281828459
Valor "verdadero"2.718281828459
D_j^(k) = D_{j+1}^(k-1) + (D_{j+1}^(k-1)-D_j^(k-1))/(8^k-1))