A Method for Solving a Multipoint BVP With a Nonlinear Integro‐Differential Operator

ABSTRACT The study examines the applicability of the Dzhumabaev parametrization method to multipoint boundary value problems for a Duffing‐type integro‐differential operator equation. The original problem is reformulated as an equivalent parametric multipoint problem, which was then decomposed into two subproblems: A nonlinear special Cauchy problem and a system of nonlinear algebraic equations. The special Cauchy problem is addressed via linearization at fixed parameter values and solved through a sequence of stepwise linear approximations. The solutions obtained are subsequently employed to construct the right‐hand side of the algebraic system and its associated Jacobi matrix. On this basis, a new approach for solving the original problem is developed. The efficiency and convergence of the proposed approach were confirmed through a numerical example.