Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation

IF 0.3 Q4 MATHEMATICS Matematika Pub Date : 2023-04-15 DOI:10.11113/matematika.v39.n1.1448
Nur Nadiah Mohd Rahan, Nur Nadiah Abd Hamid
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引用次数: 0

Abstract

Extended cubic B-spline collocation method is formulated to solve the Benjamin-Bona-Mahony equation without linearization. The Besse relaxation scheme is applied on the nonlinear terms and therefore transforms the equation into a systemof two linear equations. The time derivative is discretized using Forward Difference Approximation whereas the spatial dimension is approximated using extended cubic B-spline function. Applying the von-Neumann stability analysis, the proposed technique are shown unconditionally stable. Two numerical examples are presented and the results are compared with the exact solutions and recent methods.
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求解Benjamin-Bona-Mahony方程的Besse扩展三次B样条配置方法
为了求解Benjamin-Bona-Mahony方程,提出了一种不进行线性化的扩展三次B样条配置方法。贝塞尔松弛格式应用于非线性项,因此将方程转换为两个线性方程组。时间导数使用前向差分近似进行离散,而空间维度使用扩展的三次B样条函数进行近似。应用von Neumann稳定性分析,证明了所提出的技术是无条件稳定的。给出了两个数值例子,并将结果与精确解和最近的方法进行了比较。
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来源期刊
Matematika
Matematika MATHEMATICS-
自引率
25.00%
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0
审稿时长
24 weeks
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