Fractional Numerical Simulation of Coupled Approximate Long Wave and Modified Boussinesq Equations Involving Mittag-Leffler Kernel
Abstract
:1. Introduction
2. Preliminaries
3. Methodology
4. Numerical Examples
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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(Approx) | (Exact) | |||||
---|---|---|---|---|---|---|
0.2 | −0.244849 | −0.244844 | −0.244810 | −0.244701 | −0.2445699 | |
0.4 | −0.252178 | −0.252154 | −0.252140 | −0.252122 | −0.252119 | |
0.2 | 0.6 | −0.249632 | −0.249608 | −0.249595 | −0.249577 | −0.249574 |
0.8 | −0.247212 | −0.247188 | −0.247176 | −0.247158 | −0.247155 | |
1 | −0.244911 | −0.244888 | −0.244876 | −0.244859 | −0.244855 | |
0.2 | −0.254864 | −0.254850 | −0.254838 | −0.254818 | −0.254812 | |
0.4 | −0.252183 | −0.252169 | −0.252158 | −0.252138 | −0.252132 | |
0.4 | 0.6 | −0.249637 | −0.249623 | −0.249612 | −0.249593 | −0.249586 |
0.8 | −0.247217 | −0.247203 | −0.247193 | −0.247174 | −0.247167 | |
1 | −0.244915 | −0.244902 | −0.244892 | −0.244874 | −0.244866 | |
0.2 | −0.254868 | −0.254861 | −0.254853 | −0.254835 | −0.254826 | |
0.4 | −0.252187 | −0.252180 | −0.252172 | −0.252154 | −0.252145 | |
0.6 | 0.6 | −0.249640 | −0.249634 | −0.249626 | −0.249609 | −0.249599 |
0.8 | −0.247220 | −0.247214 | −0.247206 | −0.247189 | −0.247178 | |
1 | −0.244918 | −0.244912 | −0.244905 | −0.244889 | −0.244877 | |
0.2 | −0.254874 | −0.254870 | −0.254866 | −0.254851 | −0.254840 | |
0.4 | −0.252192 | −0.252189 | −0.252185 | −0.252171 | −0.252158 | |
0.8 | 0.6 | −0.249644 | −0.249642 | −0.249638 | −0.249624 | −0.249611 |
0.8 | −0.247226 | −0.247222 | −0.247218 | −0.247204 | −0.247190 | |
1 | −0.244923 | −0.244921 | −0.244917 | −0.244904 | −0.244889 | |
0.2 | −0.254882 | −0.254879 | −0.254878 | −0.254868 | −0.254854 | |
0.4 | −0.252199 | −0.252197 | −0.252196 | −0.252187 | −0.252171 | |
1 | 0.6 | −0.249654 | −0.249650 | −0.249649 | −0.249640 | −0.249623 |
0.8 | −0.247234 | −0.247230 | −0.247229 | −0.247220 | −0.247202 | |
1 | −0.244932 | −0.244928 | −0.244927 | −0.244919 | −0.244900 |
(Approx) | (Exact) | |||||
---|---|---|---|---|---|---|
0.2 | −0.013760 | −0.013754 | −0.013751 | −0.013747 | −0.013747 | |
0.4 | −0.013066 | −0.013061 | −0.013058 | −0.013055 | −0.013055 | |
0.2 | 0.6 | −0.012414 | −0.012410 | −0.012407 | −0.012404 | −0.012404 |
0.8 | −0.011801 | −0.011796 | −0.011794 | −0.011791 | −0.011791 | |
1 | −0.011223 | −0.011219 | −0.011217 | −0.011213 | −0.011213 | |
0.2 | −0.013761 | −0.013758 | −0.013755 | −0.013751 | −0.013751 | |
0.4 | −0.013067 | −0.013064 | −0.013062 | −0.013058 | −0.013058 | |
0.4 | 0.6 | −0.012415 | −0.012413 | −0.012411 | −0.012407 | −0.012407 |
0.8 | −0.011802 | −0.011799 | −0.011797 | −0.011794 | −0.011794 | |
1 | −0.011224 | −0.011221 | −0.011220 | −0.011216 | −0.011216 | |
0.2 | −0.013762 | −0.013760 | −0.013758 | −0.013754 | −0.013754 | |
0.4 | −0.013068 | −0.013067 | −0.013065 | −0.013061 | −0.013061 | |
0.6 | 0.6 | −0.012416 | −0.012415 | −0.012413 | −0.012410 | −0.012410 |
0.8 | −0.011803 | −0.011801 | −0.011800 | −0.011797 | −0.011797 | |
1 | −0.011225 | −0.011223 | −0.011222 | −0.011219 | −0.011219 | |
0.2 | −0.013764 | −0.013762 | −0.013761 | −0.013758 | −0.013758 | |
0.4 | −0.013071 | −0.013069 | −0.013068 | −0.013065 | −0.013065 | |
0.8 | 0.6 | −0.012419 | −0.012417 | −0.012416 | −0.012413 | −0.012413 |
0.8 | −0.011805 | −0.011803 | −0.011802 | −0.011800 | −0.011800 | |
1 | −0.011228 | −0.011225 | −0.011224 | −0.011222 | −0.011222 | |
0.2 | −0.013768 | −0.013766 | −0.013764 | −0.013762 | −0.013762 | |
0.4 | −0.013074 | −0.013071 | −0.013070 | −0.013068 | −0.013068 | |
1 | 0.6 | −0.012422 | −0.012420 | −0.012418 | −0.012416 | −0.012416 |
0.8 | −0.011808 | −0.011806 | −0.011804 | −0.011803 | −0.011803 | |
1 | −0.011230 | −0.011228 | −0.011226 | −0.011225 | −0.011225 |
(Approx) | ||||||
---|---|---|---|---|---|---|
0.2 | −0.124923 | −0.124912 | −0.124907 | −0.124899 | −0.124899 | |
0.4 | −0.123582 | −0.123572 | −0.123567 | −0.123559 | −0.123559 | |
0.2 | 0.6 | −0.122308 | −0.122299 | −0.122294 | −0.122287 | −0.122287 |
0.8 | −0.121098 | −0.121089 | −0.121084 | −0.121077 | −0.121077 | |
1 | −0.119947 | −0.119938 | −0.119934 | −0.119927 | −0.119927 | |
0.2 | −0.124925 | −0.124919 | −0.124914 | −0.124906 | −0.124906 | |
0.4 | −0.123584 | −0.123578 | −0.123574 | −0.123566 | −0.123566 | |
0.4 | 0.6 | −0.122310 | −0.122305 | −0.122300 | −0.122293 | −0.122293 |
0.8 | −0.121100 | −0.121094 | −0.121090 | −0.121083 | −0.121083 | |
1 | −0.119948 | −0.119943 | −0.119940 | −0.119933 | −0.119933 | |
0.2 | −0.124926 | −0.124924 | −0.124920 | −0.124913 | −0.124913 | |
0.4 | −0.123585 | −0.123583 | −0.123580 | −0.123572 | −0.123572 | |
0.6 | 0.6 | −0.122311 | −0.122309 | −0.122306 | −0.122299 | −0.122299 |
0.8 | −0.121101 | −0.121098 | −0.121096 | −0.121089 | −0.121089 | |
1 | −0.119950 | −0.119947 | −0.119945 | −0.119938 | −0.119938 | |
0.2 | −0.124927 | −0.124928 | −0.124926 | −0.124920 | −0.124920 | |
0.4 | −0.123588 | −0.123586 | −0.123585 | −0.123579 | −0.123579 | |
0.8 | 0.6 | −0.122315 | −0.122312 | −0.122311 | −0.122305 | −0.122305 |
0.8 | −0.121104 | −0.121102 | −0.121100 | −0.121095 | −0.121095 | |
1 | −0.119953 | −0.119950 | −0.119949 | −0.119944 | −0.119944 | |
0.2 | −0.124935 | −0.124933 | −0.124931 | −0.124927 | −0.124927 | |
0.4 | −0.123592 | −0.123590 | −0.123589 | −0.123585 | −0.123585 | |
1 | 0.6 | −0.122319 | −0.122316 | −0.122315 | −0.122311 | −0.122311 |
0.8 | −0.121107 | −0.121106 | −0.121104 | −0.121101 | −0.121101 | |
1 | −0.119958 | −0.119955 | −0.119953 | −0.119950 | −0.119950 |
(Approx) | (Exact) | |||||
---|---|---|---|---|---|---|
0.2 | −0.006880 | −0.006877 | −0.006875 | −0.006873 | −0.006873 | |
0.4 | −0.006533 | −0.006530 | −0.006529 | −0.006527 | −0.006527 | |
0.2 | 0.6 | −0.006207 | −0.006205 | −0.006203 | −0.006202 | −0.006202 |
0.8 | −0.005900 | −0.005898 | −0.005897 | −0.005895 | −0.005895 | |
1 | −0.005611 | −0.005609 | −0.005608 | −0.005606 | −0.005606 | |
0.2 | −0.006880 | −0.006879 | −0.006877 | −0.006875 | −0.006875 | |
0.4 | −0.006533 | −0.006532 | −0.006531 | −0.006529 | −0.006529 | |
0.4 | 0.6 | −0.006207 | −0.006206 | −0.006205 | −0.006203 | −0.006203 |
0.8 | −0.005901 | −0.005899 | −0.005898 | −0.005897 | −0.005897 | |
1 | −0.005612 | −0.005610 | −0.005610 | −0.005608 | −0.005608 | |
0.2 | −0.006881 | −0.006880 | −0.006879 | −0.006877 | −0.006877 | |
0.4 | −0.006534 | −0.006533 | −0.006532 | −0.006530 | −0.006530 | |
0.6 | 0.6 | −0.006208 | −0.006207 | −0.006206 | −0.006205 | −0.006205 |
0.8 | −0.005901 | −0.005900 | −0.005900 | −0.005898 | −0.005898 | |
1 | −0.005612 | −0.005611 | −0.005611 | −0.005609 | −0.005609 | |
0.2 | −0.006881 | −0.006881 | −0.006880 | −0.006879 | −0.006879 | |
0.4 | −0.006534 | −0.006534 | −0.006534 | −0.006532 | −0.006532 | |
0.8 | 0.6 | −0.006208 | −0.006208 | −0.006208 | −0.006206 | −0.006206 |
0.8 | −0.005901 | −0.005901 | −0.005901 | −0.005900 | −0.005900 | |
1 | −0.005612 | −0.005612 | −0.005612 | −0.005611 | −0.005611 | |
0.2 | −0.006881 | −0.006882 | −0.006882 | −0.006881 | −0.006881 | |
0.4 | −0.006534 | −0.006535 | −0.006535 | −0.006534 | −0.006534 | |
1 | 0.6 | −0.006208 | −0.006209 | −0.006209 | −0.006208 | −0.006208 |
0.8 | −0.005901 | −0.005902 | −0.005902 | −0.005901 | −0.005901 | |
1 | −0.005612 | −0.005613 | −0.005613 | −0.005612 | −0.005612 |
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Alderremy, A.A. Fractional Numerical Simulation of Coupled Approximate Long Wave and Modified Boussinesq Equations Involving Mittag-Leffler Kernel. Symmetry 2022, 14, 1632. https://doi.org/10.3390/sym14081632
Alderremy AA. Fractional Numerical Simulation of Coupled Approximate Long Wave and Modified Boussinesq Equations Involving Mittag-Leffler Kernel. Symmetry. 2022; 14(8):1632. https://doi.org/10.3390/sym14081632
Chicago/Turabian StyleAlderremy, Aisha Abdullah. 2022. "Fractional Numerical Simulation of Coupled Approximate Long Wave and Modified Boussinesq Equations Involving Mittag-Leffler Kernel" Symmetry 14, no. 8: 1632. https://doi.org/10.3390/sym14081632
APA StyleAlderremy, A. A. (2022). Fractional Numerical Simulation of Coupled Approximate Long Wave and Modified Boussinesq Equations Involving Mittag-Leffler Kernel. Symmetry, 14(8), 1632. https://doi.org/10.3390/sym14081632