Theory and Modern Applications

# Table 4 $$C_{2}$$-order of convergence for Test problem 3

γ = 0.1
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$9.293 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$6.869 × 10−33.76
$$h = \tau =\frac{1}{4}$$4.962 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$3.558 × 10−33.80
γ = 0.2
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$8.200 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$5.916 × 10−33.78
$$h = \tau =\frac{1}{4}$$4.298 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$3.058 × 10−33.81
γ = 0.3
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$7.092 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$5.068 × 10−33.81
$$h = \tau =\frac{1}{4}$$3.643 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$2.616 × 10−33.80
γ = 0.4
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$5.966 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$4.206 × 10−33.83
$$h = \tau =\frac{1}{4}$$2.996 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$2.171 × 10−43.80
γ = 0.5
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$4.824 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$3.402 × 10−33.82
$$h = \tau =\frac{1}{4}$$2.359 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$1.669 × 10−33.82
γ = 0.6
h/τMax error$$C_{2}$$-order
$$h =\tau =\frac{1}{2}$$3.668 × 10−2
$$h =\frac{1}{4}$$, $$\tau =\frac{1}{32}$$2.652 × 10−33.79
$$h = \tau =\frac{1}{4}$$1.735 × 10−2
$$h =\frac{1}{8}$$, $$\tau =\frac{1}{64}$$1.201 × 10−33.85