Numerical Solutions of the Gardner Equation by Extended Form of the\n Cubic B-splines

2017/02/09 by Özlem Ersoy Hepson, Hepson, Ozlem Ersoy, Alper Korkmaz +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1702.02776

openalex publication_date 2017/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The extended definition of the polynomial B-splines may give a chance to\nimprove the results obtained by the classical cubic polynomial B-splines.\nDetermination of the optimum value of the extension parameter can be achieved\nby scanning some intervals containing zero. This study aims to solve some\ninitial boundary value problems con- structed for the Gardner equation by the\nextended cubic B-spline collocation method.The test problems are derived from\nsome analytical studies to validate the efficiency and accuracy of the\nsuggested method. The conservation laws are also determined to observe them\nremain constant as expected in theoretical aspect. The stability of the\nproposed method is investigated by the Von Neumann analysis.\n

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