A NEW APPROACH FOR THE SOLUTION OF FOURTH-ORDER BOUNDARY VALUE PROBLEMS - Yesil, Ulku; Akgun, Fatma Aydin; Ozturk, Mahpeyker; Rasulov, Zaur (ROCKY MT MATH CONSORTIUM, 2025)
Many of the results on second-order boundary value problems cannot be generalized to third-and fourth-order studies because they are difficult or impossible to solve. Therefore, solving higher-order boundary value problems is still an interesting topic. For the numerical solution of higher-order boundary value problems, we demonstrate an iteration method that includes the Green's function. We obtained the necessary conditions to demonstrate the validity of the method and proved the existence and uniqueness theorems. We solved a series of numerical examples to demonstrate considered method's reliability and accuracy, and we compared our results with well-known existing methods in the literature to prove its effectiveness. Numerical calculations were made using MATLAB.
Keywords: fourth-order boundary value problem; numerical solutions; Green's function; convergence rate; iteration method; ITERATIVE METHOD; EXISTENCE; Mathematics