Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain
Abstract
1. Introduction
2. Description of Method
3. Numerical Experiment
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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t | Algorithm in [22] | Finite Element Method [22] | Cubic B-Spline Method [20] | Present Method |
---|---|---|---|---|
2 | 6.8170 × 10−3 | 9.0000 × 10−6 | 3.5753 × 10−6 | 1.7367 × 10−7 |
4 | 1.3740 × 10−2 | 1.7000 × 10−5 | 5.9568 × 10−6 | 1.9645 × 10−7 |
6 | 2.0710 × 10−2 | 2.6000 × 10−5 | 8.4798 × 10−6 | 4.1904 × 10−7 |
8 | 2.7660 × 10−2 | 3.6000 × 10−5 | 1.0519 × 10−5 | 3.8485 × 10−7 |
10 | 3.4550 × 10−2 | 4.4000 × 10−5 | 1.2062 × 10−5 | 4.6152 × 10−7 |
t | Algorithm in [22] | Finite Element Method [22] | Cubic B-Spline Method [20] | Present Method |
---|---|---|---|---|
2 | 3.9200 × 10−4 | 2.7400 × 10−4 | 2.7430 × 10−4 | 6.9387 × 10−6 |
4 | 7.8600 × 10−4 | 2.3000 × 10−4 | 2.2998 × 10−4 | 1.8324 × 10−5 |
6 | 1.1830 × 10−3 | 2.2500 × 10−4 | 2.2498 × 10−4 | 3.3104 × 10−5 |
8 | 1.5820 × 10−3 | 2.2100 × 10−4 | 2.2103 × 10−4 | 5.0898 × 10−5 |
10 | 1.9830 × 10−3 | 2.1700 × 10−4 | 2.1676 × 10−4 | 7.3263 × 10−5 |
Method | ||||
---|---|---|---|---|
Analytical | 3.9799497 | 0.81046249 | 2.579007 | |
Present method | 0.01 | 3.9799497 | 0.81046249 | 2.579007 |
Method I in [23] | 0.01 | 3.9799 | 0.8104 | 2.5790 |
Method II in [23] | 0.01 | 3.9799 | 0.8104 | 2.5790 |
Method in [24] | 0.01 | 3.97988 | 0.810453 | 2.57898 |
p | x | Exact Solution | Numerical Solution | Absolute Error |
---|---|---|---|---|
4 | −10 | 0.0094 | 0.0094 | 2.3306 × 10−12 |
−5 | 0.1147 | 0.1147 | 7.3283 × 10−11 | |
0 | 0.9379 | 0.9379 | 1.5064 × 10−9 | |
5 | 0.1310 | 0.1310 | 1.8122 × 10−10 | |
10 | 0.0108 | 0.0108 | 3.5643 × 10−12 | |
8 | −10 | 0.0081 | 0.0081 | 2.5062 × 10−12 |
−5 | 0.0992 | 0.0992 | 3.3017 × 10−10 | |
0 | 1.0515 | 1.0515 | 2.5424 × 10−9 | |
5 | 0.1133 | 0.1133 | 2.2898 × 10−10 | |
10 | 0.0093 | 0.0093 | 2.0325 × 10−12 |
p | t | Finite Difference Scheme [25] | Finite Difference Scheme [26] | Present Method |
---|---|---|---|---|
4 | 0.2 | 2.3111 × 10−3 | 2.4126 × 10−3 | 4.5129 × 10−9 |
0.4 | 4.7384 × 10−3 | 4.9448 × 10−3 | 4.9426 × 10−9 | |
0.6 | 7.1138 × 10−3 | 7.4230 × 10−3 | 5.9942 × 10−9 | |
0.8 | 9.2928 × 10−3 | 9.7015 × 10−3 | 6.9753 × 10−9 | |
1.0 | 1.1261 × 10−2 | 1.1760 × 10−2 | 5.6849 × 10−9 | |
8 | 0.2 | 1.1151 × 10−2 | 1.1290 × 10−2 | 7.5195 × 10−8 |
0.4 | 2.1295 × 10−2 | 2.2573 × 10−2 | 1.8036 × 10−7 | |
0.6 | 3.1416 × 10−2 | 3.2822 × 10−2 | 2.8450 × 10−7 | |
0.8 | 4.1946 × 10−2 | 4.2464 × 10−2 | 3.8517 × 10−7 | |
1.0 | 5.0220 × 10−2 | 5.1841 × 10−2 | 4.8838 × 10−7 |
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Zhang, W.; Wang, H.; Zhang, H.; Li, Z.; Li, X. Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain. Fractal Fract. 2024, 8, 383. https://doi.org/10.3390/fractalfract8070383
Zhang W, Wang H, Zhang H, Li Z, Li X. Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain. Fractal and Fractional. 2024; 8(7):383. https://doi.org/10.3390/fractalfract8070383
Chicago/Turabian StyleZhang, Wei, Haijing Wang, Haolu Zhang, Zhiyuan Li, and Xiaoyu Li. 2024. "Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain" Fractal and Fractional 8, no. 7: 383. https://doi.org/10.3390/fractalfract8070383
APA StyleZhang, W., Wang, H., Zhang, H., Li, Z., & Li, X. (2024). Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain. Fractal and Fractional, 8(7), 383. https://doi.org/10.3390/fractalfract8070383