Approximate Solution of the Nonlinear Buckmaster Partial Differential Equation using Exponential Fourth-order Differentiable Functions

Usman Yusuf; Moses Anayo Mbah; Collins E. Akpan; Abubakar Abdulkarim; Muhammad Sani Otto; Aminu Buhari; Godwin Ma'aji; Philip Nwanosike

doi:10.62050/ljsir2025.v3n2.564

Authors

Usman Yusuf Department of Mathematics, Federal University of Lafia, Nasarawa State Author
Mbah Moses Anayo Department of Mathematics, Federal University of Lafia, Nasarawa State Author
Akpan Collins E. Department of Mathematics, Federal University of Lafia, Nasarawa State Author
Abubakar Abdulkarim Department of Mathematics, Ahmadu Bello University, Zaria, Kaduna State Author
Muhammad Sani Otto Department of Physics, Federal University of Lafia, Nasarawa State Author
Aminu Buhari Department of Mathematics, Federal University of Lafia, Nasarawa State Author
Godwin Ma'aji Department of Mathematics, Federal University of Lafia, Nasarawa State Author
Philip Nwanosike Department of Mathematics, Federal University of Lafia, Nasarawa State Author

DOI:

https://doi.org/10.62050/ljsir2025.v3n2.564

Keywords:

Buckmaster equation, Collocation method, Exponential cubic B-splines, Partial differential equations, Splines

Abstract

In this paper, the nonlinear partial differential equation, Buckmaster equation is solved using the exponential cubic B-spline collocation method (ECBSM) and the approximate solutions from this method are compared with those of the hybrid cubic B-spline collocation method (HCBSM). In order to solve the equation, linearization technique is needed to linearize the nonlinear terms of the equation. This is done by the Taylor’s expansion approach. Further, the linearized equation is discretized into the fully implicit scheme and the Crank-Nicolson scheme. Three examples are used to test the proposed schemes by the fully implicit and Crank-Nicolson methods. The absolute errors of the methods are calculated and the comparison between the results of the ECBSM and the HCBSM is carried out. This is to analyze the accuracy of the methods of approximation. Both the ECBSM and HCBSM possess a free parameter which aids in determining accurate results. In general, the methods proved reliable with accuracy in approximating solutions of the equation.

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