aspg-33-2881-1792223535 20261017075215 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2024 10 2 Ahmed R. Khlefha Department of Mathematics, College of Education, University of Sumer, Thi-Qar, Iraq. This research dealt with the study of the boundary values associated with differential equations, which are of the non-linear and third-order type. A new algorithm was created that uses exponential spline functions to study and address boundary value problems of a general nature. We have demonstrated that the numerical approach used, which was built using exponential spline functions, gives us good and accurate results for these problems, which have been compared to existing numerical methods. We found that the proposed method is accurate and effective compared to other Spalline methods. 2024 52 60 2881 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0100205 https://americaspg.com/journal/33/article/2881 https://americaspg.com/storage/21718359791.pdf