ليث الناصري

This thesis presents the development an‎d analysis of a sixth-order numerical scheme for solving general nonlinear fifth-order two-point boundary value problems (BVPs). Traditional approaches employing stan‎dard sixtic spline approximations typically yield only O(h^2) accuracy, resulting in suboptimal numerical performance. To overcome this limitation, a new method based on high-order perturbations of the original problem is proposed. These perturbations are systematically incorporated to construct a numerical algorithm with significantly enhanced accuracy. The proposed scheme achieves a global error of order O(h^6), an‎d a rigorous convergence analysis is carried out to establish its theoretical foundation. The method is also extended to han‎dle systems of nonlinear fifth-order two-point BVPs. Comprehensive numerical experiments are conducted to assess the computational performance of the method, an‎d the results confirm the theoretical predictions regarding the order of convergence. The proposed high-order scheme demonstrates both accuracy an‎d robustness, making it a promising tool for the numerical solution of high-order nonlinear boundary value problems.

مسائل مقدار مرزي غيرخطي دو نقطه اي مرتبه پنجم , همگرايي , شبيه‌سازي عددي

Fifth-order two-point nonlinear boundary value problems (BVPs) , Convergence , Numerical method

Laith Juma Fadhel AL-Nasiri

Jalil Rahshidinia