Articles written in Pramana – Journal of Physics
Volume 91 Issue 4 October 2018 Article ID 0059 Research Article
Numerical solutions of the Gardner equation by extended form of the cubic B-splines
OZLEM ERSOY HEPSON ALPER KORKMAZ IDRIS DAG
The extended definition of the polynomial B-splines may give a chance to improve the results obtained by the classical cubic polynomial B-splines. The optimum value of the extension parameter can be determined by scanning some intervals containing zero. This study aims to solve some initial boundary value problems constructed for the Gardner equation by the extended cubic B-spline collocation method. The test problems are derived from some analytical studies to validate the efficiency and accuracy of the suggested method. The conservation laws are also determined to observe whether the test problems remain constant as expected from the theoretical aspect. The stability of the proposed method is investigated by the von Neumann analysis.
Volume 96 All articles Published: 19 January 2022 Article ID 0030 Research Article
A higher-order efficient approach to numerical simulations of the RLW equation
IDRIS DAG OZLEM ERSOY HEPSON BÜLENT SAKA
A new numerical algorithm for solving the regularised long wave (RLW) equation is proposed using predictor–corrector method in time and quartic B-spline collocation procedure in space. Accuracy of algorithm is shown by studying the motion of a single solitary wave. Interaction of two solitary waves and three solitary waves, and wave generation from Maxwellian condition are performed to illustrate the suitability of the proposed scheme. Results of the present method are compared with the outcomes of some prosperous numerical algorithms.
Volume 97, 2023
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