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Theory and Modern Applications

Table 1 The computational results to the first problem at \(y=0.5, x,y \in [0,1]\)

From: A new structure to n-dimensional trigonometric cubic B-spline functions for solving n-dimensional partial differential equations

x

Numerical results

Exact results

Absolute error

Quadratic B-Spline [17]

0.1

0.36864

0.36949

8.50648 E-4

1.06992 E-3

0.2

0.80030

0.80230

2.00391 E-3

2.32385 E-3

0.3

1.28317

1.28617

2.99684 E-3

3.40917 E-3

0.4

1.79152

1.79535

3.83645 E-3

4.31609 E-3

0.5

2.27966

2.28422

4.55318 E-3

5.04294 E-3

0.6

2.67314

2.67835

5.21325 E-3

5.60652 E-3

0.7

2.85650

2.86243

5.93213 E-3

6.05466 E-3

0.8

2.65688

2.66375

6.87164 E-3

6.46809 E-3

0.9

1.82191

1.83010

8.19215 E-3

6.93102 E-3