In this paper, we propose an idea how the differential transformation, a semi-analytical approach based on Taylor’s theorem, can be used to find an approximation of the unique solution to the boundary value problem for partial differential equations of elliptic type. We focus on two-dimensional equations with initial conditions given at the sides of a square. The considered differential equation is transformed into a recurrence relation in two variables. Solving the recurrence relation using the boundary conditions leads to an infinite system of linear equations with infinitely many variables. Approximation of the solution is given in the form of two-dimensional Taylor polynomial whose coefficients are determined by solution to a truncated system of linear equations. Boundary value problem consisting of the Laplace equation and Dirichlet boundary conditions has been chosen to demonstrate relevance of the idea to the given problem.

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