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Theory and Modern Applications

Table 7 Comparison between the absolute errors for Example 4

From: A new generalized Jacobi Galerkin operational matrix of derivatives: two algorithms for solving fourth-order boundary value problems

x

GJCOMM ( N  = 4)

GJCOMM ( N  = 6)

GJCOMM ( N  = 8)

RKHSM ( \(\boldsymbol {u^{101}_{1}}\) ) [38]

0.0

0.0

0.0

0.0

0.0

0.1

1.74774 × 10−11

2.42005 × 10−14

9.34812 × 10−17

2.78 × 10−8

0.2

8.7269 × 10−11

1.5889 × 10−14

8.29415 × 10−18

8.09 × 10−8

0.3

2.27345 × 10−11

3.59562 × 10−14

2.17857 × 10−18

1.20 × 10−7

0.4

1.213 × 10−10

6.36858 × 10−14

6.03901 × 10−17

1.25 × 10−7

0.5

6.32272 × 10−12

1.87133 × 10−15

2.06595 × 10−16

9.56 × 10−8

0.6

1.27768 × 10−10

6.44606 × 10−14

1.21431 × 10−17

4.82 × 10−8

0.7

1.44017 × 10−11

4.09586 × 10−14

1.10589 × 10−16

7.38 × 10−9

0.8

9.92086 × 10−11

1.56333 × 10−14

8.74301 × 10−16

1.07 × 10−8

0.9

2.37061 × 10−11

2.57225 × 10−14

3.38271 × 10−17

7.08 × 10−9

1.0

4.44089 × 10−16

2.70617 × 10−16

2.27249 × 10−16

0.0