Solving Nonlinear Benjamin-Bona-Mahony Equation Using Cubic B-spline and Cubic Trigonometric B-spline Collocation Methods

被引：3

作者：

Rahan, Nur Nadiah Mohd ^{[1
]}

Ishak, Siti Noor Shahira ^{[1
]}

Abd Hamid, Nur Nadiah ^{[1
]}

Abd Majid, Ahmad ^{[1
]}

Azmi, Amirah ^{[1
]}

机构：

[1] Univ Sains Malaysia, Sch Math Sci, Gelugor 11800, Penang, Malaysia

来源：

4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS4): MATHEMATICAL SCIENCES: CHAMPIONING THE WAY IN A PROBLEM BASED AND DATA DRIVEN SOCIETY | 2017年 / 1830卷

关键词：

D O I：

10.1063/1.4980895

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this research, the nonlinear Benjamin-Bona-Mahony (BBM) equation is solved numerically using the cubic B-spline (CuBS) and cubic trigonometric B-spline (CuTBS) collocation methods. The CuBS and CuTBS are utilized as interpolating functions in the spatial dimension while the standard finite difference method (FDM) is applied to discretize the temporal space. In order to solve the nonlinear problem, the BBM equation is linearized using Taylor's expansion. Applying the von-Neumann stability analysis, the proposed techniques are shown to be unconditionally stable under the Crank-Nicolson scheme. Several numerical examples are discussed and compared with exact solutions and results from the FDM.

引用

页数：6

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