The structural method for Ordinary Differential Equations
For researchers in numerical analysis and scientific computing, this method offers a novel approach to ODE solving, but the abstract lacks concrete performance comparisons or benchmarks, making it incremental.
The paper introduces a new numerical method for solving ODE systems that computes approximations of solutions and their derivatives up to order K over a block of R time steps, achieving high accuracy and good spectral resolution.
We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order $K$ by solving an entire block corresponding to $R$ time steps. We build the physical relations that connect the function and derivative approximations at each time step by using the ODE and its derivatives, and develop the structural equations that establish linear relations between the function and its derivative over the whole block of $R$ times steps. The non-linear system is solved and provide very accurate approximations with nice spectral resolution properties.