The extended B-spline collocation method for numerical solutions of Fisher equation

2015 ◽  
Author(s):  
O. Ersoy ◽  
I. Dağ
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Fisher Equation ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method

scholarly journals The exponential cubic B-spline collocation method for the Kuramoto-Sivashinsky equation

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 853-861 ◽  
Author(s):  
Ozlem Ersoy ◽  
Idiris Dag
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Spline Approximation ◽  
Algebraic Equations ◽  
Spline Collocation ◽  
Fully Integrated ◽  
B Spline ◽  
Spline Collocation Method ◽  
Sivashinsky Equation ◽  
Good Agreement

In this study the Kuramoto-Sivashinsky (KS) equation has been solved using the collocation method, based on the exponential cubic B-spline approximation together with the Crank Nicolson. KS equation is fully integrated into a linearized algebraic equations. The results of the proposed method are compared with both numerical and analytical results by studying two text problems. It is found that the simulating results are in good agreement with both exact and existing numerical solutions.

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.

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