A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method
References
- Burden R.L., Faires J.D., Numerical Analysis, PWS Publishing Company, Boston, USA, 1993.
- Benjamin T.B., Bona J.L., Mahony J.J., Model equations for long waves in nonlinear dispersive systems, Philosophical Transactions of the Royal Society of London, 272, 47–78, 1972.
- Korteweg D.J., Vries D.G., XLI On the change of the form of long waves advancing in a rectangular channel and on a new type of long stationary wave, The London Edinburgh and Dublin Philosophical Magazine and Journal of Science, 39(240), 422–443, 1895.
- Kumbinarasaiah S., Raghunatha K.R., Rezazadeh M., Inc M., A solution of coupled nonlinear differential equations arising in a rotating micropolar nanofluid flow system by Hermite wavelet technique, Engineering with Computers, 38, 3351–3372, 2022.
- Rogers C., Shadwich W.F., Bäcklund Transformations and Their Application, Academic Press, New York, USA, 1982.
- Kumbinarasaiah S., Mulimani M., A novel scheme for the hyperbolic partial differential equation through Fibonacci wavelets, Journal of Taibah University for Science, 16(1), 1112–1132, 2022.
- Kumbinarasaiah S., Mulimani M., Fibonacci wavelets-based numerical method for solving fractional order (1+1)-dimensional dispersive partial differential equation, International Journal of Dynamics and Control, DOI:10.1007/s40435-023-01129-12023, 2023.
- Kumbinarasaiah S., Mulimani M., Fibonacci wavelets approach for the fractional Rosenau-Hyman equations, Results in Control and Optimization, 11, 100221, 2023.
- Abbasbandy S., Shirzadi A., The first integral method for modified Benjamin-Bona-Mahony equation, Communications in Nonlinear Science and Numerical Simulation, 15, 1759–1764, 2010.
- Hirota R., Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Physical Review Letters, 27, 1192–1194, 1971.
- Kumbinarasaiah S., Mulimani M., A study on the nonlinear Murray equation through the Bernoulli wavelet approach, International Journal of Applied and Computational Mathematics, 9(3), 40, 2023.
- Ganji Z.Z., Ganji D.D., Bararnia H., Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method, Applied Mathematical Modelling, 33, 1836–1841, 2009.
- Kumbinarasaiah S., Numerical solution for the (2+1)-dimensional Sobolev and regularized long wave equations arise in fluid mechanics via wavelet technique, Partial Differential Equations in Applied Mathematics, 3, 100016, 2021.
- Shiralashetti S.C., Angadi L.M., Deshi A.B., Kantli M.H., Haar wavelet method for the numerical solution of Benjamin-Bona-Mahony equations, Journal of Information and Computing Science, 11(2), 136–145, 2016.
- Abd-Elhameed W.M., Youssri Y.H., New ultraspherical wavelets spectral solutions for fractional Riccati differential equations, Abstract and Applied Analysis, 2014(ID:626275), 1–8, 2014.
- Doha E.H., Abd-Elhameed W.M., Youssri Y.H., New ultraspherical wavelets collocation method for solving 2nth-order initial and boundary value problems, Journal of the Egyptian Mathematical Society, 24, 319–327, 2016.
- Abd-Elhameed W.M., Youssri Y.H., New solutions for singular Lane-Emden equations arising in astrophysics based on shifted ultraspherical operational matrices of derivatives, Computational Methods for Differential Equations, 2(3), 171–185, 2014.
- Kumbinarasaiah S., Mulimani M., Comparative study of Adomian decomposition method and Clique polynomial method, Partial Differential Equations in Applied Mathematics, 6, 100454, 2022.
- Kumbinarasaiah S., Mundewadi R.A., Wavelets approach for the solution of nonlinear variable delay differential equations, International Journal of Mathematics and Computers in Engineering, 1(2), 49–58, 2023.
- Li F., Baskonus H.M., Kumbinarasaiah S., Manohara G., Gao W., Ilhan E., An efficient numerical scheme for biological models in the frame of Bernoulli wavelets, Computer Modeling in Engineering and Sciences, 137(3), 2381–2408, 2023.
- Tanriverdi T., Baskonus H.M., Mahmud A.A., Muhamad K.A., Explicit solution of fractional order atmosphere-soil-land plant carbon cycle system, Ecological Complexity, 48, 100966, 2021.
- Baskonus H.M., Mahmud A.A., Muhamad K.A., Tanriverdi T., Gao W., Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles, Thermal Science, 26(2), 1229–1244, 2022.
- Baskonus H.M., Mahmud A.A., Muhamad K.A., Tanriverdi T., A study on Caudrey-Dodd-Gibbon-Sawada-Kotera partial differential equation, Mathematical Methods in the Applied Sciences, 45(14), 8737–8753, 2022.
- Mahmud A.A., Tanriverdi T., Muhamad K.A., Baskonus H.M., Structure of the analytic solutions for the complex nonlinear (2+1)-dimensional conformable time-fractional Schrödinger equation, Thermal Science, 27, 211–225, 2023.
- Mahmud A.A., Tanriverdi T., Muhamad K.A., Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods, International Journal of Mathematics and Computer in Engineering, 1(1), 11–24, 2023.
- Mahmud A.A., Baskonus H.M., Tanriverdi T., Muhamad K.A., Optical solitary waves and soliton solutions of the (3+1)-dimensional generalized Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation, Computational Mathematics and Mathematical Physics, 63(6), 1085–1102, 2023.
- Mahmud A.A., Tanriverdi T., Muhamad K.A., Baskonus H.M., Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation, Journal of Applied Mathematics and Computational Mechanics, 22(2), 36–48, 2023.
DOI: https://doi.org/10.2478/ijmce-2024-0014 | Journal eISSN: 2956-7068
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
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© 2024 Mallanagoud Mulimani, Kumbinarasaiah Srinivasa, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.