Abstract
We introduce a family of multivalue almost collocation methods with diagonal coefficient matrix for the numerical solution of ordinary differential equations. The choice of this type of coefficient matrix permits a reduction of the computational cost and a parallel implementation. Collocation gives a continuous extension of the solution which is useful for a variable step size implementation. We provide examples of A-stable methods with two and three stages and order 3.
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The authors are members of the GNCS group. This work is supported by GNCS-INDAM project and by PRIN2017-MIUR project.
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Conte, D., D’Ambrosio, R., D’Arienzo, M.P., Paternoster, B. (2020). Multivalue Almost Collocation Methods with Diagonal Coefficient Matrix. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12249. Springer, Cham. https://doi.org/10.1007/978-3-030-58799-4_10
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