Abstract
In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework is based on an expansion of the vector field along an orthonormal basis, and relies on perturbation results for the considered problem. Initially devised for the approximation of ordinary differential equations, it is here further extended and, moreover, generalized to cope with constant delay differential equations. Relevant classes of Runge-Kutta methods can be derived within this framework.
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Brugnano, L., Frasca-Caccia, G., Iavernaro, F. et al. A new framework for polynomial approximation to differential equations. Adv Comput Math 48, 76 (2022). https://doi.org/10.1007/s10444-022-09992-w
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DOI: https://doi.org/10.1007/s10444-022-09992-w
Keywords
- Ordinary differential equations
- Delay differential equations
- Orthogonal polynomials
- Local Fourier expansion
- Polynomial approximations
- Runge-Kutta methods