Literature

The below literature is only a subset of the relevant research papers and books. If you are familiar with a reference that you think is important to the topic of mixture approximations, please add it to the below list.

Distributed time delays (mixture approximations)

T.K.S. Ritschel, 2025. On Erlang Mixture Approximations for Differential Equations with Distributed Time Delays. arXiv: 2502.12984. DOI (code): 10.5281/zenodo.15685296. In submission.

N. Guglielmi and E. Hairer, 2025. Applying stiff integrators for ordinary differential equations and delay differential equations to problems with distributed delays, SIAM Journal on Scientific Computing, 47, pp. A102–A123. DOI: 10.1137/24M1632413.

T.K.S. Ritschel, J. Wyller, 2025. An Algorithm for Distributed Time Delay Identification without A Priori Knowledge of the Kernel. Automatica 178, pp. 112382. arXiv: 2405.07328. DOI (code): 10.5281/zenodo.10001583. DOI: 10.1016/j.automatica.2025.112382.

Distributed time delays (linear chain trick)

H. Smith, 2011. An introduction to delay differential equations with applications to the life sciences, vol. 57 of Texts in Applied Mathematics, Springer. DOI: 10.1007/978-1-4419-7646-8.

N. MacDonald, 1978. Time lags in biological models, vol. 27 of Lecture Notes in Biomathematics, Springer. DOI: 10.1007/978-3-642-93107-9.

A. Ponosov, A. Shindiapin, and J. J. Miguel, 2002. The W-transform links delay and ordinary differential equations, Functional Differential Equations, 9, pp. 437–469.

Functional differential equations

V. Kolmanovskii, A. Myshkis, 1999. Introduction to the Theory and Applications of Functional Differential Equations, vol. 463 of Mathematics and Its Applications, Springer. DOI: 10.1007/978-94-017-1965-0.

J. K. Hale and S. M. V. Lunel, 1993. Introduction to functional differential equations, vol. 99 of Applied Mathematical Sciences, Springer. DOI: 10.1007/978-1-4612-4342-7.

V. Kolmanovskii and A. Myshkis, 1992. Applied theory of functional differential equations, vol. 85 of Mathematics and Its Applications, Springer. DOI: 10.1007/978-94-015-8084-7.

Convergence of mixture approximations

J. Korevaar, 1968. Mathematical methods, vol. 1, Academic Press.