We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the solutions. We show by numerical tests that these schemes are numerically robust and computationally efficient.

翻译：本文提出了一种新方法，用于求解巴拿赫空间中带有非局部边界条件的某些演化方程。基于该方法，我们推导出一族数值格式以近似求解。数值测试表明，这些格式具有数值鲁棒性和计算高效性。