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A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method Cover

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

International Journal of Mathematics and Computer in Engineering
Volume 2 (2024): Issue 2 (December 2024)
By: Mallanagoud Mulimani and  Kumbinarasaiah Srinivasa  
Open Access
|Jan 2024
Figures & tables

Figures & Tables

Fig. 1

Comparison of the projected scheme solution with other solutions for Problem 1 at t=19 t = {1 \over 9} .

Fig. 2

Graphical demonstration of the solution of present and other methods for Problem 1.

Fig. 3

Comparison of the projected scheme solution with other solutions for Problem 2 at t=16 t = {1 \over 6} .

Fig. 4

Graphical demonstration of the solution of present and other methods for Problem 2.

Fig. 5

Comparison of the projected scheme solution with other solutions for Problem 3 at t=16 t = {1 \over 6} .

Fig. 6

Graphical demonstration of the solution of present and other methods for Problem 3.

Comparison of the projected scheme with other techniques for N = M = 8 of Problem 2_

x = (/16)FDM [14]HWM [14]UWMExact
11.157419351.207500771.205865821.20623024
31.357500431.369264981.36585291.36683794
51.578814321.551090391.54738501.54883029
71.824348281.756391701.75333081.75505465
92.097446321.988920881.98694091.98873746
112.401857582.252809542.25189872.25353478
132.741790962.552574922.55237832.55358945
153.121976592.893084582.89310912.89359594

Comparison of the projected scheme with other techniques for N = M = 8 of Problem 3_

x = (/16)FDM [14]UWMExact
10.058872800.056586190.05555555
30.176670110.169667620.16666666
50.294623660.282474220.27777777
70.412841520.394816450.38888888
90.531437720.506495070.50000000
110.650535000.617297000.61111111
130.770267630.726990790.72222222
150.890784690.835321750.83333333

Comparison of the projected scheme with other techniques for N = M = 8 of Problem 1_

x = (/16)FDM [14]HWM [14]UWMExact
10.829422540.829576750.828878680.82902911
30.732779570.732444940.731240410.73161562
50.647568780.646217710.645140420.64564852
70.572453820.569950690.569223440.56978282
90.506256040.502670600.502293440.50283157
110.447935980.443424970.443294940.44374731
130.396577110.391306810.391296480.39160562
150.351371420.345466590.345476050.34559075

AE of the present scheme for Problem 3_

xAE at M = 6AE at M = 7AE at M = 8AE at M = 9
0.12.1089 × 10−31.8448 × 10−31.6396 × 10−31.5825 × 10−3
0.24.0983 × 10−33.5849 × 10−33.1859 × 10−32.9895 × 10−3
0.35.8473 ×10−35.1141 ×10−34.5446 ×10−33.1664 ×10−3
0.47.2314 × 10−36.3236 × 10−35.6186 × 10−34.8969 × 10−3
0.58.1208 × 10−37.0998 ×10−36.3072 × 10−35.9892 ×10−3
0.68.3788 ×10−37.3234 ×10−36.5045 ×10−36.3058 ×10−3
0.77.8595 ×10−36.8674 × 10−36.0980 × 10−35.2771 ×10−3
0.86.4062 ×10−35.5955 × 10−34.9672 × 10−33.7137 ×10−3
0.93.8484 ×10−33.3601 × 10−32.9818 × 10−31.0753 ×10−3

AE of the present scheme for Problem 1_

xAE at M = 6AE at M = 7AE at M = 8AE at M = 9
0.13.9376 × 10−42.9425 × 10−42.2818 × 10−41.8209 × 10−4
0.26.7769 × 10−45.0624 × 10−43.9246 × 10−43.1312 × 10−4
0.38.6162 ×10−46.4339 ×10−44.9864 ×10−43.9775 ×10−4
0.49.5446 × 10−47.1244 × 10−45.5200 × 10−44.4021 × 10−4
0.59.6427 × 10−47.1949 ×10−45.5729 × 10−44.4433 ×10−4
0.68.9835 ×10−46.7003 ×10−45.1883 ×10−44.1357 ×10−4
0.77.6329 ×10−45.6907 × 10−44.4052 × 10−43.5106 ×10−4
0.85.6505 ×10−44.2109 × 10−43.2587 × 10−42.5963 ×10−4
0.93.0900 ×10−42.3018 × 10−41.7807 × 10−41.4184 ×10−4

AE of the present scheme for Problem 2_

xAE at M = 6AE at M = 7AE at M = 8AE at M = 9
0.11.0354 × 10−37.4856 × 10−45.6626 × 10−44.4325 × 10−4
0.21.8990 × 10−31.3729 × 10−31.0386 × 10−38.1295 × 10−4
0.32.5727 ×10−31.8600 ×10−31.4070 ×10−31.1014 ×10−3
0.43.0365 × 10−32.1953 × 10−31.6607 × 10−31.2999 × 10−3
0.53.2684 × 10−32.3630 ×10−31.7875 × 10−31.3992 ×10−3
0.63.2441 ×10−32.3454 ×10−31.7742 ×10−31.3888 ×10−3
0.72.9364 ×10−32.1230 × 10−31.6060 × 10−31.2571 ×10−3
0.82.3157 ×10−31.6742 × 10−31.2665 × 10−39.9137 ×10−4
0.91.3490 ×10−39.7533 × 10−47.3780 × 10−45.7753 ×10−4
DOI: https://doi.org/10.2478/ijmce-2024-0014 | Journal eISSN: 2956-7068
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Language: English
Page range: 179 - 192
Submitted on: Jul 27, 2023
Accepted on: Sep 6, 2023
Published on: Jan 10, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Benjamin-Bona-Mahony equation,
ultraspherical wavelet,
collocation method
Related subjects:
Computer sciences,
Computer sciences, other,
Engineering,
Introductions and overviews,
Engineering, other,
Mathematics,
General mathematics,
Physics,
Physics, other

© 2024 Mallanagoud Mulimani, Kumbinarasaiah Srinivasa, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 2 (2024): Issue 2 (December 2024)
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