def bvp(epsilon, subintervals): # for figure2.pdf X,Y = fd_order2_ode(func=lambda x:-1.,a1=lambda x:epsilon, a2=lambda x:-1.,a3=lambda x:0., a=0.,b=1., alpha=1.,beta=3.,N=subintervals) return X,Y
def bvp(epsilon, subintervals): def g(x): out = -epsilon*pi**2.*cos(pi*x) - pi*x*sin(pi*x) return out X,Y = fd_order2_ode(func=g,a1=lambda x:epsilon, a2=lambda x: x,a3=lambda x:0., a=-1.,b=1., alpha=-2.,beta=0.,N=subintervals) return X,Y
def bvp(epsilon, subintervals): # X,Y = fd_order2_ode(func=lambda x: 0.,a1=lambda x:1., # a2=lambda x: 4.*x/(epsilon+x**2.),a3=lambda x:2./(epsilon+x**2.), # a=-1.,b=1., alpha=1./(1.+epsilon), # beta=1./(1.+epsilon),N=subintervals) X,Y = fd_order2_ode(func=lambda x: 0.,a1=lambda x:(epsilon+x**2.), a2=lambda x: 4.*x,a3=lambda x:2., a=-1.,b=1., alpha=1./(1.+epsilon), beta=1./(1.+epsilon),N=subintervals) return X,Y
def bvp(epsilon, subintervals):
# for figure3.pdf
X, Y = fd_order2_ode(func=lambda x: np.cos(x),
a1=lambda x: epsilon,
a2=lambda x: 0.,
a3=lambda x: -4. * (np.pi - x**2.),
a=0.,
b=np.pi / 2.,
alpha=0.,
beta=1.,
N=subintervals)
return X, Y
def bvp(epsilon, subintervals):
# for figure3.pdf
X, Y = fd_order2_ode(
func=lambda x: np.cos(x),
a1=lambda x: epsilon,
a2=lambda x: 0.0,
a3=lambda x: -4.0 * (np.pi - x ** 2.0),
a=0.0,
b=np.pi / 2.0,
alpha=0.0,
beta=1.0,
N=subintervals,
)
return X, Y
