Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem

Kukreja, Vijay Kumar; ., Shallu

doi:10.22034/cmde.2024.49824.2071

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	Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem
Computational Methods for Differential Equations
مقاله 16، دوره 13، شماره 2، خرداد 2025، صفحه 578-591 اصل مقاله (2.46 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.49824.2071
نویسندگان
Vijay Kumar Kukreja^* ؛ Shallu .
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Punjab, India.
چکیده
This study employs the cubic B-spline collocation strategy to address the solution challenges posed by the nonlinear generalized Burgers-Fisher’s equation (gBFE), with some improvisation. This approach incorporates refinements within the spline interpolants, resulting in enhanced convergence rates along the spatial dimension. Temporal integration is achieved through the Crank-Nicolson methodology. The stability of the technique is assessed using the rigorous von Neumann method. Convergence analysis based on Green’s function reveals a fourth-order convergence along the space domain and a second-order convergence along the temporal domain. The results are validated by taking a number of examples. MATLAB 2017 is used for computational work.
کلیدواژه‌ها
Burgers-Fisher’s equation؛ B-splines collocation method؛ Crank Nicolson؛ Convergence analysis؛ Stability analysis

مراجع
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Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem