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Theory and Modern Applications

Table 2 Comparison between the relative errors for Example 1

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

x

1OM [35]

2OMs [35]

GJGOMM ( N  = 8)

GJGOMM ( N  = 12)

0.25

5.39791 × 10−3

8.11851 × 10−3

1.09077 × 10−10

2.75173 × 10−15

0.50

1.57835 × 10−2

2.09205 × 10−2

1.14685 × 10−10

1.33747 × 10−15

0.75

2.54797 × 10−2

2.93281 × 10−2

8.24739 × 10−11

4.50799 × 10−16

1.00

3.14713 × 10−2

3.09264 × 10−2

3.3689 × 10−12

5.37406 × 10−16

1.25

3.22814 × 10−2

2.65317 × 10−2

7.75226 × 10−11

2.27451 × 10−16

1.50

2.73173 × 10−2

1.82938 × 10−2

9.08649 × 10−11

2.54606 × 10−15

1.75

1.64910 × 10−2

8.68533 × 10−3

7.53861 × 10−11

9.75198 × 10−16