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

共 50 条

[41] Cubic B-Spline Interpolation and Realization
Wang, Zhijiang
Wang, Kaili
An, Shujiang
[J]. INFORMATION COMPUTING AND APPLICATIONS, PT I, 2011, 243 : 82 - 89
[42] An efficient cubic B-spline and bicubic B-spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations
Mirzaee, Farshid
Alipour, Sahar
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (01) : 384 - 397
[43] Cubic spline interpolation with quasiminimal B-spline coefficients
László, L
[J]. ACTA MATHEMATICA HUNGARICA, 2005, 107 (1-2) : 77 - 87
[44] Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method
Kukreja, V. K.
[J]. JOURNAL OF OCEAN ENGINEERING AND SCIENCE, 2022, 7 (02) : 99 - 111
[45] MODIFIED CUBIC B-SPLINE INTERPOLATION
HSI, P
LEE, CH
[J]. PROCEEDINGS OF THE IEEE, 1981, 69 (12) : 1590 - 1592
[46] Cubic B-spline differential quadrature methods and stability for Burgers' equation
Korkmaz, Alper
Dag, Idris
[J]. ENGINEERING COMPUTATIONS, 2013, 30 (03) : 320 - 344
[47] Cubic spline interpolation with quasiminimal B-spline coefficients
Lajos László
[J]. Acta Mathematica Hungarica, 2005, 107 : 77 - 87
[48] Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation
Singh, Swarn
Bhatt, Sandeep
Singh, Suruchi
[J]. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (01): : 28 - 43
[49] A COLLOCATION SOLUTION FOR BURGERS-EQUATION USING CUBIC B-SPLINE FINITE-ELEMENTS
ALI, AHA
GARDNER, GA
GARDNER, LRT
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 100 (03) : 325 - 337
[50] Solving Coupled Nonlinear Schrodinger Equations using Cubic B-spline Interpolation and Finite Difference Methods
Anuar, Hanis Safirah Saiful
Azmi, Amirah
Abd Hamid, Nur Nadiah
Abd Majid, Ahmad
[J]. PROCEEDING OF THE 25TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM25): MATHEMATICAL SCIENCES AS THE CORE OF INTELLECTUAL EXCELLENCE, 2018, 1974

← 1 2 3 4 5 →