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Kukreja, Vijay Kumar, ., Shallu. (1403). Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem. سامانه مدیریت نشریات علمی, 13(2), 578-591. doi: 10.22034/cmde.2024.49824.2071
Vijay Kumar Kukreja; Shallu .. "Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem". سامانه مدیریت نشریات علمی, 13, 2, 1403, 578-591. doi: 10.22034/cmde.2024.49824.2071
Kukreja, Vijay Kumar, ., Shallu. (1403). 'Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem', سامانه مدیریت نشریات علمی, 13(2), pp. 578-591. doi: 10.22034/cmde.2024.49824.2071
Kukreja, Vijay Kumar, ., Shallu. Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem. سامانه مدیریت نشریات علمی, 1403; 13(2): 578-591. doi: 10.22034/cmde.2024.49824.2071

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
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