finite_differences.py 文件源码

def compute_stencil(order, n, x_value, h_value, x0=0.):
    """
    computes a stencil of Order order
    """
    h,x = symbols('h x')
    xs = [x+h*cos(i*pi/n) for i in range(n,-1,-1)]
    cs = finite_diff_weights(order, xs, x0)[order][n]
    cs = [simplify(c) for c in cs]

    cs = [simplify(expr.subs(h, h_value)) for expr in cs]
    xs = [simplify(expr.subs(h, h_value)) for expr in xs]

    cs = [simplify(expr.subs(x, x_value)) for expr in cs]
    xs = [simplify(expr.subs(x, x_value)) for expr in xs]

    return xs, cs

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