scholarly journals Hyperbolic-trigonometric tension B-spline Galerkin approach for the solution of Fisher equation

2021 ◽  
Author(s):  
Idris Dag ◽  
Ozlem Ersoy Hepson
Keyword(s):  
Fisher Equation ◽  
Galerkin Approach ◽  
B Spline

The exponential cubic B-spline algorithm for Fisher equation

2016 ◽  
Vol 86 ◽  
pp. 101-106 ◽  
Author(s):  
Idiris Dag ◽  
Ozlem Ersoy
Keyword(s):  
Fisher Equation ◽  
B Spline

The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

2019 ◽  
Vol 10 (01) ◽  
pp. 1941007
Author(s):  
A. K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Galerkin Finite Element Method ◽  
Approximation Solution ◽  
Test Function ◽  
Galerkin Finite Element ◽  
Galerkin Approach ◽  
B Spline ◽  
Variational Iteration ◽  
Appl Math

In this paper, time-fractional Sharma–Tasso–Olver (STO) equation has been solved numerically through the Petrov–Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function. The Petrov–Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically. The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method (VIM) and exact solutions. For fractional order, the numerical outcomes of fractional Sharma–Tasso–Olver equations are also compared with those obtained by variational iteration method (VIM) in Song et al. [Song L., Wang Q., Zhang H., Rational approximation solution of the fractional Sharma–Tasso–Olver equation, J. Comput. Appl. Math. 224:210–218, 2009]. Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.

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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