University of Tabriz Computational Methods for Differential Equations 2345-3982 13 2 2025 03 01 Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem 578 591 18047 10.22034/cmde.2024.49824.2071 EN Vijay Kumar Kukreja Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Punjab, India. Shallu . Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Punjab, India. Journal Article 2022 01 08 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. https://cmde.tabrizu.ac.ir/article_18047_3a4b56857b6b868498b181431e9998ec.pdf