Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term

Table 2

The maximum error and temporal convergence order by Numerical Scheme II (see (61)).

α		The maximum error	The temporal convergence order
1.1	1ℎ=51,𝜏=50	5.030598𝑒−004	—
	1ℎ=51,𝜏=100	1.398353𝑒−004	1.8470
	1ℎ=51,𝜏=200	4.521910𝑒−005	1.6287
	1ℎ=51,𝜏=400	2.132246𝑒−005	1.0846
1.2	1ℎ=61,𝜏=50	4.445704𝑒−004	—
	1ℎ=61,𝜏=100	1.173968𝑒−004	1.9210
	1ℎ=61,𝜏=200	3.399818𝑒−005	1.7879
	1ℎ=61,𝜏=400	1.295545𝑒−005	1.3919
1.3	1ℎ=51,𝜏=50	3.816458𝑒−004	—
	1ℎ=71,𝜏=100	9.909362𝑒−005	1.9454
	1ℎ=71,𝜏=200	2.713495𝑒−005	1.8686
	1ℎ=71,𝜏=400	8.986675𝑒−006	1.5943
1.4	1ℎ=51,𝜏=50	3.193648𝑒−004	—
	1ℎ=81,𝜏=100	8.224534𝑒−005	1.9572
	1ℎ=81,𝜏=200	2.186799𝑒−005	1.9111
	1ℎ=81,𝜏=400	6.641262𝑒−006	1.7193
1.5	1ℎ=110,𝜏=50	2.574223𝑒−004	—
	1ℎ=110,𝜏=100	6.580906𝑒−005	1.9678
	1ℎ=110,𝜏=200	1.700153𝑒−005	1.9526
	1ℎ=110,𝜏=400	4.689779𝑒−006	1.8581
1.6	1ℎ=115,𝜏=50	1.972538𝑒−004	—
	1ℎ=115,𝜏=100	5.020982𝑒−005	1.9740
	1ℎ=115,𝜏=200	1.272752𝑒−005	1.9800
	1ℎ=115,𝜏=400	3.268637𝑒−006	1.9612
1.7	1ℎ=120,𝜏=50	1.402871𝑒−004	—
	1ℎ=120,𝜏=100	3.570742𝑒−005	1.9741
	1ℎ=120,𝜏=200	9.023412𝑒−006	1.9845
	1ℎ=120,𝜏=400	2.285957𝑒−006	1.9809
1.8	1ℎ=120,𝜏=50	8.770513𝑒−005	—
	1ℎ=120,𝜏=100	2.235014𝑒−005	1.9724
	1ℎ=120,𝜏=200	5.655983𝑒−006	1.9824
	1ℎ=120,𝜏=400	1.438349𝑒−006	1.9754
1.9	1ℎ=120,𝜏=50	4.067501𝑒−005	—
	1ℎ=120,𝜏=100	1.038309𝑒−005	1.9699
	1ℎ=120,𝜏=200	2.636242𝑒−006	1.9777
	1ℎ=120,𝜏=400	6.778414𝑒−007	1.9595