TY - JOUR
T1 - Two Reliable Computational Techniques for Solving the MRLW Equation
AU - Al-Khaled, Kamel
AU - Jafer, Haneen
N1 - Publisher Copyright:
© 2023 by the authors.
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PY - 2023/2/8
Y1 - 2023/2/8
N2 - In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equation by a classic finite difference formula, while the space derivatives are approximated by a (Formula presented.) weighted scheme. For comparison purposes, we also find a soliton solution using the Adomian decomposition method (ADM). The Sinc-collocation method was were found to be more accurate and efficient than the ADM schemes. Furthermore, we show that the number of solitons generated can be approximated using the Maxwellian initial condition. The proposed methods’ results, analytical solutions, and numerical methods are compared. Finally, a variety of graphical representations for the obtained solutions makes the dynamics of the MRLW equation visible and provides the mathematical foundation for physical and engineering applications.
AB - In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equation by a classic finite difference formula, while the space derivatives are approximated by a (Formula presented.) weighted scheme. For comparison purposes, we also find a soliton solution using the Adomian decomposition method (ADM). The Sinc-collocation method was were found to be more accurate and efficient than the ADM schemes. Furthermore, we show that the number of solitons generated can be approximated using the Maxwellian initial condition. The proposed methods’ results, analytical solutions, and numerical methods are compared. Finally, a variety of graphical representations for the obtained solutions makes the dynamics of the MRLW equation visible and provides the mathematical foundation for physical and engineering applications.
KW - Adomian decomposition method
KW - MRLW equation
KW - sinc-collocation method
KW - soliton solutions
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U2 - 10.3390/axioms12020174
DO - 10.3390/axioms12020174
M3 - Article
AN - SCOPUS:85148873216
SN - 2075-1680
VL - 12
SP - 174
JO - Axioms
JF - Axioms
IS - 2
M1 - 2
ER -