Analysis of Nonlocal Problem for Loaded Parabolic Equation via Numerical Method

This paper investigates a nonlocal problem for a loaded parabolic equation defined on a closed domain. By applying spatial discretization, the original problem is transformed into a two-point boundary value problem for a system of loaded ordinary differential equations. To address this problem, the Dzhumabaev parameterization method is utilized. Based on this approach, a numerical algorithm is developed to solve the original problem. The effectiveness of the proposed method is demonstrated through two computational examples. The obtained numerical results are compared with the exact solutions to validate the accuracy of the algorithm.