Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2881 2022 2022 Department of Mathematics, College of Education, University of Sumer, Thi-Qar, Iraq. Ahmed Ahmed 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 2024 52 60 10.54216/GJMSA.0100205 https://www.americaspg.com/articleinfo/33/show/2881