Numerical solutions of the EW and MEW equations using a fourth-order improvised B-spline collocation method

A fourth-order improvised cubic B-spline collocation method (ICSCM) is proposed to numerically solve the equal width (EW) equation and the modified equal width (MEW) equation. The discretization of the spatial domain is done using the ICSCM and the Crank-Nicolson scheme is used for the discretizatio...

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Veröffentlicht in:Numerical algorithms Jg. 98; H. 4; S. 1799 - 1825
Hauptverfasser: Fan, Guangyu, Wu, Beibei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2025
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Approximation
B spline functions
Boundary conditions
Collocation methods
Computer Science
Crank-Nicholson method
Discretization
Exact solutions
Fourier series
Mathematical analysis
Methods
Norms
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Solitary waves
Stability analysis
Theory of Computation
Wave propagation
Stability
EW and MEW equations
Gauss elimination method
Cubic B-spline method
Crank-Nicolson scheme
ISSN:1017-1398, 1572-9265
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Zusammenfassung:A fourth-order improvised cubic B-spline collocation method (ICSCM) is proposed to numerically solve the equal width (EW) equation and the modified equal width (MEW) equation. The discretization of the spatial domain is done using the ICSCM and the Crank-Nicolson scheme is used for the discretization of the temporal domain. The nonlinear terms are processed using quasi-linearization techniques and the stability analysis of this method is performed using Fourier series analysis. The validity and accuracy of this method are verified through several numerical experiments using a single solitary wave, two solitary waves, Maxwellian initial condition, and an undular bore. Since there is an exact solution for the single wave, the error norms L 2 and L ∞ are first calculated and compared with some previous studies published in journal articles. In addition, the three conserved quantities Q , M , and E of the problems raised during the simulation are also calculated and recorded in the table. Lastly, the comparisons of these error norms and conserved quantities show that the numerical results obtained with the proposed method are more accurate and agree well with the values of the conserved quantities obtained in some literatures using the same parameters. The main advantage of ICSCM is its ability to effectively capture solitary wave propagation and describe solitary wave collisions. It can perform solution calculations at any point in the domain, easily use larger time steps to calculate solutions at higher time levels, and produce more accurate calculation results.
Bibliographie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01853-5