The article considers a nonlocal boundary value problem for a third-order partial differential equation. This problem is reduced to a nonlocal boundary value problem for integro-differential equations with partial derivatives. Next, the parameterization method proposed in the works of D.S. Dzhumabaev is employed to solve a two-point boundary value problem for an ordinary differential equation. The paper proposes an algorithm for finding an approximate solution based on solving these local problems. Convergence conditions of the proposed algorithm are derived, along with accuracy estimates comparing approximate solutions with exact ones. The results of the study have theoretical significance and can be used to find approximate solutions to nonlocal boundary problems for third-order equations that arise in various fields of science and technology.
Orumbayeva et al. (2025) studied this question.