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Theory and Modern Applications

Table 2 Convergence rates of the ETDRK4-P13 scheme in time

From: Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation

τ

α = 1.2

α = 1.6

α = 1.8

Avg. CPU (s)

e(τ)

p

e(τ)

p

e(τ)

p

1/100

1.2388e−2

3.989

1.3319e−2

4.005

1.2256e−2

3.996

2.4631

1/200

7.8010e−4

4.006

8.2984e−4

4.011

7.6792e−4

4.021

4.7275

1/400

4.8544e−5

4.012

5.1479e−5

4.007

4.7315e−5

4.015

8.6160

1/800

3.0095e−6

3.2014e−6

2.9261e−6

15.2435

1/1600

29.0225