We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli-Silvestre extension and diagonalization. Our scheme uses the analytic solution to the associated eigenvalue problem in the extended dimension. We show its relation to a quadrature scheme. Numerical examples demonstrate the performance of the method.

翻译：我们提出了一种基于Caffarelli-Silvestre延拓与对角化技术的谱分数拉普拉斯算子近似求解方法。该方案利用扩展维度上相关特征值问题的解析解，并揭示了其与数值积分格式的关联。数值算例验证了该方法的计算性能。