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Theory and Modern Applications

Table 3 The errors of the first zero between numerical solutions and exact solution of ( 5.2 )

From: Oscillation of Runge-Kutta methods for advanced impulsive differential equations with piecewise constant arguments

m

Explicit Euler

Trapezoidal rule

Implicit Euler

AE

RE

AE

RE

AE

RE

100

0.0020

0.0025

9.1599e − 06

1.1672e − 05

0.0020

0.0025

200

9.9290e − 04

0.0013

2.2900e − 06

2.9180e − 06

9.9369e − 04

0.0013

400

4.9657e − 04

6.3277e − 04

5.7249e − 07

7.2951e − 07

4.9673e − 04

6.3296e − 04

800

2.4833e − 04

3.1644e − 04

1.4312e − 07

1.8238e − 07

2.4832e − 04

3.1643e − 04

1,600

1.2418e − 04

1.5824e − 04

3.3076e − 08

4.2148e − 08

1.2421e − 04

1.5828e − 04

3,200

6.2108e − 05

7.9142e − 05

8.2691e − 09

1.0537e − 08

6.2109e − 05

7.9144e − 05

Ratio

1.9992

1.9992

4.0654

4.0654

2.0009

2.0009