We study the implementation of a Chebyshev spectral method with forward Euler integrator to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper.

翻译：我们研究了采用Chebyshev谱方法与向前Euler积分器相结合的方法，以探究Richards方程的一种近场动力学非局部形式。通过利用近似解的紧致性性质及数值格式的稳定性，我们证明了该模型完全离散化的收敛性，并展示了该方法弱形式解的存在性与唯一性。此外，我们通过数值模拟进一步验证了理论结果，采用不同光滑阶次的初始条件，证明了本文所提出理论结果的可靠性和稳健性。