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

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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

x	Finite difference method (Dehghan 2006)	Tau method (Saadatmandi and Dehghan 2011)	Present method
x	m = 5	Tau method (Saadatmandi and Dehghan 2011)	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