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.
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Kukreja, V. K. and ., S. (2025). Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem. Computational Methods for Differential Equations, 13(2), 578-591. doi: 10.22034/cmde.2024.49824.2071
MLA
Kukreja, V. K. , and ., S. . "Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem", Computational Methods for Differential Equations, 13, 2, 2025, 578-591. doi: 10.22034/cmde.2024.49824.2071
HARVARD
Kukreja, V. K., ., S. (2025). 'Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem', Computational Methods for Differential Equations, 13(2), pp. 578-591. doi: 10.22034/cmde.2024.49824.2071
CHICAGO
V. K. Kukreja and S. ., "Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem," Computational Methods for Differential Equations, 13 2 (2025): 578-591, doi: 10.22034/cmde.2024.49824.2071
VANCOUVER
Kukreja, V. K., ., S. Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem. Computational Methods for Differential Equations, 2025; 13(2): 578-591. doi: 10.22034/cmde.2024.49824.2071
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