Analytic and numerical solutions for linear and nonlinear multidimensional wave equations
Joint Authors
al-Jawari, Majid Ahmad
Ravnik, J.
Adwan, M. I.
Tibaut, J.
Source
Arab Journal of Basic and Applied Sciences
Issue
Vol. 27, Issue 1 (30 Jun. 2020), pp.165-182, 18 p.
Publisher
University of Bahrain College of Science
Publication Date
2020-06-30
Country of Publication
Bahrain
No. of Pages
18
Main Subjects
Abstract EN
We develop three reliable iterative methods for solving the nonlinear 1D, 2D and 3D second-order wave equation and compare the results with a discretization-based solver.
The iterative Tamimi–Ansari method (TAM), Daftardar–Jafari method (DJM) and the Banach contraction method (BCM) are used to obtain the exact solution for linear equations.
For nonlinear equations and practical problems, however, one obtains the approximate solutions that converge to the exact solution, if one exists.
The convergence analysis of the three methods is shown using the fixed-point theorem.
The methods prove to be quite efficient and well suited to solve this kind of problems.
We present several examples that demonstrate the accuracy and efficiency of the methods.
We also compare the methods with a method based on discretization (Boundary Domain Integral Method (BDIM)).
The BDIM uses a standard domain grid and discretizes the integral form of the governing equations.
The iterative methods were developed with Mathematica® 10, while BDIM is a proprietary development.
American Psychological Association (APA)
Adwan, M. I.& al-Jawari, Majid Ahmad& Tibaut, J.& Ravnik, J.. 2020. Analytic and numerical solutions for linear and nonlinear multidimensional wave equations. Arab Journal of Basic and Applied Sciences،Vol. 27, no. 1, pp.165-182.
https://search.emarefa.net/detail/BIM-957398
Modern Language Association (MLA)
Adwan, M. I.…[et al.]. Analytic and numerical solutions for linear and nonlinear multidimensional wave equations. Arab Journal of Basic and Applied Sciences Vol. 27, no. 1 (2020), pp.165-182.
https://search.emarefa.net/detail/BIM-957398
American Medical Association (AMA)
Adwan, M. I.& al-Jawari, Majid Ahmad& Tibaut, J.& Ravnik, J.. Analytic and numerical solutions for linear and nonlinear multidimensional wave equations. Arab Journal of Basic and Applied Sciences. 2020. Vol. 27, no. 1, pp.165-182.
https://search.emarefa.net/detail/BIM-957398
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 181-182
Record ID
BIM-957398