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Theory and Modern Applications

Table 1 The Coefficients of cubic B-splines and their derivatives at knots \(z_{j}\)

From: A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions

z

\(z_{j-2}\)

\(z_{j-1}\)

\(z_{j}\)

\(z_{j+1}\)

\(z_{j+2}\)

\(B_{j}(z)\)

0

\(\frac{1}{6} \)

\(\frac{4}{6}\)

\(\frac{1}{6}\)

0

\(B'_{j}(z)\)

0

\(\frac{1}{2h}\)

0

\(-\frac{1}{2h}\)

0

\(B''_{j}(z)\)

0

\(\frac{1}{h^{2}}\)

\(-\frac{2}{h^{2}}\)

\(\frac{1}{h^{2}}\)

0