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Theory and Modern Applications

Table 4 The errors of the third 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

7.1229e − 04

9.1599e − 06

3.2893e − 06

0.0020

7.1532e − 04

200

9.9290e − 04

3.5655e − 04

2.2900e − 06

8.2233e − 07

9.9369e − 04

3.5683e − 04

400

4.9657e − 04

1.7832e − 04

5.1768e − 07

1.8590e − 07

4.9673e − 04

1.7837e − 04

800

2.4833e − 04

8.9173e − 05

6.8482e − 08

2.4592e − 08

2.4832e − 04

8.9172e − 05

1,600

1.2418e − 04

4.4594e − 05

3.3076e − 08

1.1878e − 08

1.2421e − 04

4.4604e − 05

3,200

6.2108e − 05

2.2303e − 05

5.6725e − 09

2.0370e − 09

6.2109e − 05

2.2303e − 05

Ratio

1.9992

1.9992

4.7769

4.7769

2.0009

2.0009