A semi-periodic boundary value problem for a pseudo-parabolic equation of special type is investigated. A modification of the Euler polygonal method is applied to a semi-periodic boundary-value problem for a non-classical differential equation of third order. By introducing new unknown functions, the problem under consideration is reduced to an equivalent problem consisting of a family of periodic boundary value problems for a system of two ordinary differential equations and some integral relations. We obtain the conditions for the unique solvability of the problem. The estimates of convergence of approximate solution of the equivalent problem to the exact solution of the original problem are established.

中文翻译：

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求解特殊类型伪抛物方程半周期边值问题的Euler多边形方法的修改

研究了一种特殊类型的伪抛物方程的半周期边值问题。对三阶非经典微分方程，将Euler多边形方法的一种修改形式应用于半周期边值问题。通过引入新的未知函数，所考虑的问题简化为等效问题，该问题由两个常微分方程和某些积分关系的系统的一系列周期边值问题组成。我们获得了问题唯一解决的条件。建立了等效问题的近似解与原始问题的精确解的收敛性估计。