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Table 1 Comparison of the absolute error of the Fibonacci polynomial solution (u N (x, t)) and improved Fibonacci polynomial solution (u N,M (x, t)) with other methods for the same order polynomial solutions at t = 2 for Example 1

From: Numerical solutions and error estimations for the space fractional diffusion equation with variable coefficients via Fibonacci collocation method

x Finite difference method
(Dehghan 2006)
Tau method
(Saadatmandi and Dehghan 2011)
Present method
m = 5 N = 6 N, M = 6, 7
0.1 4.20e−5 4.47e−6 1.35e−6 1.89e−7
0.2 3.76e−5 2.78e−7 1.46e−6 4.01e−7
0.3 8.44e−5 5.81e−6 4.09e−7 5.41e−7
0.4 3.27e−5 1.02e−5 1.49e−6 6.02e−7
0.5 3.61e−5 1.17e−5 3.76e−6 6.11e−7
0.6 1.94e−5 1.08e−5 5.84e−6 5.92e−7
0.7 2.95e−5 8.54e−6 7.07e−6 5.49e−7
0.8 4.92e−5 6.06e−6 6.86e−6 4.58e−7
0.9 2.83e−5 3.67e−6 4.65e−6 2.84e−7