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LOW-STORAGE INTEGRAL DEFERRED CORRECTION METHODS FOR SCIENTIFIC COMPUTING
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DOI：10.1137/18M117368X.png)
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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.
Keyword:
integral deferred correction
fully implicit methods
low-storage methods
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