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Theory and Modern Applications

Table 2 Comparison of the AEs for Example 5.2 with \(\upsilon (t)=t \)

From: Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations

M

t

Proposed method

Method of [37]

5

0.1

4.39175e − 3

3.17089e − 3

0.3

1.54003e − 3

4.38223e − 4

0.5

3.13373e − 4

3.33008e − 3

0.7

2.45949e − 4

3.03242e − 2

0.9

2.29803e − 4

2.02549e − 1

6

0.1

2.87601e − 4

1.31233e − 3

0.3

4.15540e − 5

1.28026e − 4

0.5

1.33728e − 5

3.72545e − 3

0.7

8.30744e − 5

2.64696e − 2

0.9

8.30885e − 5

1.81576e − 1

7

0.1

2.76736e − 6

8.24676e − 4

0.3

1.16055e − 6

9.11265e − 5

0.5

1.01844e − 5

1.25615e − 3

0.7

1.09912e − 5

9.57862e − 3

0.9

1.10564e − 5

8.65824e − 2