SPLINE BASED NUMERICAL ALGORITHM FOR SOLVING BRATU-TYPE EQUATIONS

Saima Latif; Muhammad Amin; Saima Mushtaq; Nouman Iftikhar

doi:10.71146/kjmr446

Authors

Saima Latif Faculty of Sciences, The Superior University Lahore, Pakistan Author
Muhammad Amin Faculty of Sciences, The Superior University Lahore, Pakistan Author
Saima Mushtaq Faculty of Sciences, The Superior University Lahore, Pakistan Author
Nouman Iftikhar Faculty of Sciences, The Superior University Lahore, Pakistan Author

DOI:

https://doi.org/10.71146/kjmr446

Keywords:

Cubic B-spline, Nonlinear-boundary value problems, dependent solutions, Numerical methods, Computational efficiency, Bvp4c solver, Nonlinear equations

Abstract

This study explores the use of cubic B-spline collocation method for the numerical solution of well-known Bratu-Type Equations. The method's performance is evaluated against the widely used bvp4c solver. Numerical outcomes are compared to known exact solutions. Findings show that the cubic B-spline method consistently produces highly accurate results across various parameter values, maintaining minimal error even in cases involving strong nonlinearities. The numerical solutions closely align with the analytical solutions, confirming the method’s robustness. In addition, the approach demonstrates excellent computational efficiency. Overall, the cubic B-spline collocation method proves to be a reliable, efficient and accurate tool for solving such nonlinear boundary value problems.