The numerical study of advection–diffusion equations by the fourth-order cubic B-spline collocation method

2020 ◽  
Vol 14 (4) ◽  
pp. 409-423
Author(s):  
R. C. Mittal ◽  
Rajni Rohila
Keyword(s):  
Collocation Method ◽  
Fourth Order ◽  
Numerical Study ◽  
Diffusion Equations ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Advection Diffusion

scholarly journals A fourth-order B-spline collocation method for nonlinear Burgers–Fisher equation

2020 ◽  
Vol 14 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Aditi Singh ◽  
Sumita Dahiya ◽  
S. P. Singh
Keyword(s):  
Collocation Method ◽  
Fourth Order ◽  
Numerical Study ◽  
Fisher Equation ◽  
Spline Collocation ◽  
Von Neumann ◽  
B Spline ◽  
Spline Collocation Method ◽  
The Stability ◽  
Nicolson Scheme

AbstractA fourth-order B-spline collocation method has been applied for numerical study of Burgers–Fisher equation, which illustrates many situations occurring in various fields of science and engineering including nonlinear optics, gas dynamics, chemical physics, heat conduction, and so on. The present method is successfully applied to solve the Burgers–Fisher equation taking into consideration various parametric values. The scheme is found to be convergent. Crank–Nicolson scheme has been employed for the discretization. Quasi-linearization technique has been employed to deal with the nonlinearity of equations. The stability of the method has been discussed using Fourier series analysis (von Neumann method), and it has been observed that the method is unconditionally stable. In order to demonstrate the effectiveness of the scheme, numerical experiments have been performed on various examples. The solutions obtained are compared with results available in the literature, which shows that the proposed scheme is satisfactorily accurate and suitable for solving such problems with minimal computational efforts.

scholarly journals An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Turgut Ak ◽  
Halil Zeybek
Keyword(s):  
Collocation Method ◽  
Present Method ◽  
Numerical Study ◽  
Test Problems ◽  
Initial Condition ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Long Wave ◽  
Method Show

A septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error normsL2andL∞and the invariantsI1,I2, andI3. Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.

Sign in / Sign up

Export Citation Format

Share Document