Local radial basis functions and scale-3 Haar wavelets operational matrices based numerical algorithms for generalized regularized long wave model

• Published in: Wave motion Vol. 109; p. 102846
• Main Author: Pandit, Sapna
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2022; Elsevier BV
• Subjects: Algorithms; Discretization; Finite difference method; Generalized regularized long wave model; Linear equations; Mathematical models; Numerical analysis; Radial basis function; Radial basis functions; Scale-3 Haar wavelets; Stability; Stability analysis; Surface waves; Truncation errors; Wavelet transforms; Radial basis functions; Stability; Generalized regularized long wave model; Scale-3 Haar wavelets
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2021.102846

In this article, two numerical algorithms are designed for the simulation of generalized regularized long wave (GRLW) model via local radial basis functions (LRBFs) and Scale-3 Haar wavelets (S3HWs). First of all, the well-posedness of the model is discuss for the initial data u0x∈H02Ω. After that in the design of two numerical algorithms, the first step is semi-discretization in time with a finite difference, quasilinearization technique (QT) for linearization and then the obtained semi-discrete model is analyzed for truncation errors and stability. In the end, the semi-discrete model is fully discretized via LRBFs and S3HWs. Finally, the fully discretized system is simulated by developing MATLAB routines. In the last section, some numerical problems are considered to inspect the chastity of the developed algorithms.