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Theory and Modern Applications

Table 6 The numerical results for the test problem at \(z=y=0.5, x,y,z \in [0,1]\)

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

x

Numerical solution

Exact solution

Absolute error

Quadratic B-spline method [17]

0.1

0.0168722

0.0168984

2.62605 E-5

3.24947 E-5

0.2

0.0331474

0.0332012

5.37881 E-5

6.49943 E-5

0.3

0.0480777

0.0481595

8.18473 E-5

9.65554 E-5

0.4

0.0607169

0.0608280

1.11061 E-4

1.27075 E-4

0.5

0.0698822

0.0700264

1.44153 E-4

1.57835 E-4

0.6

0.0741084

0.0742955

1.87066 E-4

1.92337 E-4

0.7

0.0715951

0.0718456

2.50500 E-4

2.37433 E-4

0.8

0.0601448

0.0604965

3.51653 E-4

3.04639 E-4

0.9

0.0370926

0.0376082

5.15536 E-4

4.11161 E-4