The authors develop an algorithm for solving linear second-order boundary value problems with general mixed boundary conditions. It is assumed that there exists a mapping of the considered domain to a square. The proposed algorithm is a combination of the mapping method and the method of support operators [see, e.g., A. P. Favorskii, A. A. Samarskii, M. Yu. Shashkov and V. F. Tishkin, Differential Equations 17, 854-862 (1982; Zbl 0485.65060)].
First, the considered boundary value problem is transformed to a boundary value problem in a square. The new problem is of the same type as the original problem. Then, the support operator method is used to discretize the transformed problem on a uniform grid. The second-order accuracy of the method is shown by numerical examples.