Higher Order Approximation of the First Initial Boundary Value Problem for a Non-Classical Differential Equation of Hyperbolic Type
Автор: Beshtokov M.K.
Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu
Рубрика: Математика и механика
Статья в выпуске: 3 т.28, 2025 года.
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The first initial-boundary value problem for a non-classical wave equation with variable coefficients is studied. For the numerical solution of the original problem on a uniform grid, a difference scheme of increased order of accuracy is constructed, approximating the original problem. An a priori estimate in the difference interpretation is obtained by the method of energy inequalities. As a result of the analysis, an a priori estimate was obtained in difference form using the method of energy inequalities. This estimate allows us to draw conclusions about the uniqueness of the solution to the difference problem and the continuous dependence of the solution on the input data, as well as about the convergence of the numerical solution of the difference problem to the solution of the original differential problem with in the rate of O(h 4 + τ 2).
First initial-boundary value problem, wave equation, non-classical equation, numerical solution, difference scheme, a priori estimate, stability and convergence of schemes
Короткий адрес: https://sciup.org/149149339
IDR: 149149339 | УДК: 519.63 | DOI: 10.15688/mpcm.jvolsu.2025.3.1