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Highly accurate collocation methodology for solving the generalized Burgers–Fisher’s equation

Year: 2024

Type: article

Abstract: An improvised collocation scheme is applied for the numerical treatment of the nonlinear generalized Burgers–Fisher’s (gBF) equation using splines of degree three. In the proposed methodology, some subsequent rectifications are done in the spline interpolant, which resulted in the magnification of the order of convergence along the space direction. A finite difference approach is followed to integrate the time direction. Von Neumann methodology is opted to discuss the stability of the method. The error bounds and conver-gence study show that the technique has (s4 + ∆t2) order of convergence. The correspondence between the approximate and analytical solutions is shown by graphs, plotted using MATLAB and by evaluating absolute error.

Source: DOAJ (DOAJ: Directory of Open Access Journals)

DOI: 10.22067/ijnao.2024.86994.1398

Authors: S. Shallu, V.K. Kukreja

Institutions: Punjab Engineering College, Sant Longowal Institute of Engineering and Technology

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6944970713

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