Have a personal or library account? Click to login

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:
Open Access
|Jan 2024

Figures & Tables

Fig. 1

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

Previous articleVolume 2 (2024): Issue 2 (December 2024)Next article