A comparison of pseudospectral algorithms with Padе and polynomial approximations is conducted in terms of their ability to accurately solve boundary value problems for partial differential equations. For clarity, the Dirichlet problem for the Poisson equation is used. It is shown that the accuracy of the first algorithm for moderate function gradients in the boundary conditions is close to the rounding error in double precision format, while for larger gradients, it is two orders of magnitude more accurate than the second algorithm. The first algorithm is more efficient in terms of required computer memory.
Keywords: Poisson equation, Dirichlet boundary value problem, collocation and least squares method, Pade approximation, multipoint approximation, pseudospectral method, condition number of SLAE
Received January 17, 2026
Revised January 26, 2026
Accepted February 2, 2026
Vasilii P. Shapeev, Dr. Phys.-Math. Sci., Assoc. Prof., Senior Researcher, Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia, e-mail: v.shapeev@g.nsu.ru
Boris V. Semisalov, Dr. Phys.-Math. Sci., Assoc. Prof. of the Faculty of Computational Mathematics and Cybernetics of Shenzhen MSU-BIT University, Senior Researcher, Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia, e-mail: vibis87@gmail.com
Lev I. Kutkin, Novosibirsk State University, Novosibirsk, 630090 Russia, e-mail: l.kutkin@g.nsu.ru
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Cite this article as: V.P. Shapeev, B.V. Semisalov, L.I. Kutkin. Comparison of Pade and polynomial approximations for solutions of the Poisson equation. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 1, pp. 273–285.
