In this work, we study the numerical approximation of the initial-boundary-value problem of nonlinear pseudo-parabolic equations with Dirichlet boundary conditions. We propose a discretization in space with spectral schemes based on Jacobi polynomials and in time with robust schemes attending to qualitative features such as stiffness and preservation of strong stability for a more correct simulation of non-regular data. Error estimates for the corresponding semidiscrete Galerkin and collocation schemes are derived. The performance of the fully discrete methods is analyzed in a computational study.

中文翻译：

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具有时间强稳定性保持特性的伪抛物线模型的频谱离散化分析

在这项工作中，我们研究了具有 Dirichlet 边界条件的非线性伪抛物线方程的初边界值问题的数值近似。我们建议在空间中使用基于雅可比多项式的频谱方案进行离散化，并及时使用稳健方案来处理定性特征，例如刚度和保持强稳定性，以便更正确地模拟非常规数据。推导出相应的半离散 Galerkin 和搭配方案的误差估计。在计算研究中分析了完全离散方法的性能。