High Order Predictor–Corrector Cubic B-Spline Collocation Method for Modeling Solitary Waves

IF 0.8 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2023-11-25 DOI:10.1007/s40010-023-00861-9

Bülent Saka, Ozlem Ersoy Hepson, İdris Dağ

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Abstract

A collocation method with an approximate function consisting of a combination of cubic B-spline functions was established to solve the regularized long wave (RLW) equation. To increase accuracy of the method, multi-step predictor–corrector time integrator is introduced to discretize the RLW equation. The space decomposition of the dependent variable and its derivatives of the RLW equation was accomplished via the B-spline collocation method. Open form of Adams-Bashforth-Moulton method is used as a predictor, then closed Adams-Bashforth-Moulton method is implemented as a corrector. Collocation predictor–corrector method provides an increase in accuracy. Comparison is made with results of some former studies. When high accuracy time discretization is used in getting the solution of the RLW equation, it is observed that the errors are more accurate than the results of the Crank-Nicolson finite element methods listed in the article.

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孤立波建模的高阶预测校正三次b样条配点法

建立了一种由三次b样条函数组合的近似函数的配置方法来求解正则化长波方程。为了提高方法的精度，引入了多步预测校正时间积分器对RLW方程进行离散化。采用b样条配点法对RLW方程的因变量及其导数进行空间分解。采用Adams-Bashforth-Moulton方法的开放形式作为预测器，然后采用Adams-Bashforth-Moulton方法作为校正器。搭配预测校正方法提高了准确率。并与前人的研究结果进行了比较。当采用高精度时间离散法求解RLW方程时，其误差比文中列出的Crank-Nicolson有限元法的结果更精确。

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