Tommaso Buvoli, Univeristy of California, Merced
Time-dependent partial differential equations are widely used to develop accurate mathematical descriptions for a range of physical phenomena. As the scale and complexity of these models increases, so too does the need for efficient computational methods. In this work, we introduce a time-integration framework based on interpolating pol nomials in the complexplane. The use of polynomials eliminates the complexity of order conditions, enabling simple construction of methods with a specific architecture (parallel or serial), degree of implicitness ( explicit, diagonally implicit, fully implicit) and desired order of accuracy. This allows one to derive integrators that satisfy the stability and accuracy requirements of a specific application problem, and appropriately leverage a specific computer architecture.
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