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

Table 1

The maximum error and temporal and spatial convergence orders by Numerical Algorithm I (see (38)).

𝛼		The maximum error	Temporal convergence order	Spatial convergence order
1.1	1ℎ=41,𝜏=2	8.057755𝑒−002	—	—
	1ℎ=81,𝜏=8	9.573435𝑒−003	1.5366	3.0733
	1ℎ=116,𝜏=32	6.103333𝑒−004	1.9857	3.9714
	1ℎ=132,𝜏=128	3.827561𝑒−005	1.9976	3.9951
	1ℎ=164,𝜏=512	2.394875𝑒−006	1.9992	3.9984
1.3	1ℎ=41,𝜏=2	8.079213𝑒−002	—	—
	1ℎ=81,𝜏=8	1.170294𝑒−002	1.3937	2.7873
	1ℎ=116,𝜏=32	7.818506𝑒−004	1.9519	3.9038
	1ℎ=132,𝜏=128	5.015017𝑒−005	1.9813	3.9626
	1ℎ=164,𝜏=512	3.166977𝑒−006	1.9925	3.9851
1.5	1ℎ=41,𝜏=2	7.117932𝑒−002	—	—
	1ℎ=81,𝜏=8	1.300290𝑒−002	1.2263	2.4526
	1ℎ=116,𝜏=32	9.519179𝑒−004	1.8859	3.7719
	1ℎ=132,𝜏=128	6.385188𝑒−005	1.9490	3.8980
	1ℎ=164,𝜏=512	4.135300𝑒−006	1.9743	3.9487
1.7	1ℎ=41,𝜏=2	5.069482𝑒−002	—	—
	1ℎ=81,𝜏=8	1.157045𝑒−002	1.0657	2.1314
	1ℎ=116,𝜏=32	9.766015𝑒−004	1.7833	3.5665
	1ℎ=132,𝜏=128	7.054045𝑒−005	1.8956	3.7912
	1ℎ=164,𝜏=512	4.819461𝑒−006	1.9358	3.8715
1.9	1ℎ=41,𝜏=2	1.938949𝑒−002	—	—
	1ℎ=81,𝜏=8	4.643245𝑒−003	1.0310	2.0621
	1ℎ=116,𝜏=32	5.122387𝑒−004	1.5901	3.1802
	1ℎ=132,𝜏=128	4.251159𝑒−005	1.7954	3.5909
	1ℎ=164,𝜏=512	3.231450𝑒−006	1.8588	3.7176