Low-Storage Integral Deferred Correction Methods for Scientific Computing

In this work, we present a modification of the traditional integral deferred correction (IDC) approach that significantly reduces the storage requirements of the methods. These methods, which we call low-storage IDC or LS-IDC methods, require storing only one copy of each stage vector throughout the iteration process, whereas traditional IDC methods require two copies of each vector. We prove that LS-IDC methods converge with the same formal order of accuracy as traditional IDC methods as the timestep size approaches zero for the case of linear, constant-coefficient systems. A collection of numerical tests are used to evaluate the stability properties of the low-storage methods, and a nonlinear ODE and a linear transport equation are used to compare the accuracy and storage requirements of LS-IDC integrators with other fully implicit schemes. The results demonstrate that LS-IDC methods have similar accuracy but significantly reduced memory requirements compared to other fully implicit methods.