International Journal of New Developments in Engineering and Society, 2020, 4(2); doi: 10.25236/IJNDES.040220.
JiaXing NanYang Polytechnic Institute, JiaXing 563000, China
Ordinary differential equations are the process of turning practical problems into mathematical languages. They can simplify the processing of problems and promote the solution of problems. They are an important tool for linking mathematical theory with practice. Based on a brief description of mathematical modeling, this paper proposes the method steps of establishing an ordinary differential equation model, and combines the practical exploration of the application of ordinary differential equations in mathematical modeling to provide guidance for similar research.
Mathematical modeling, Ordinary differential equations, Applications
Meng Liu. Applications of Ordinary Differential Equations in Mathematical Modeling. International Journal of New Developments in Engineering and Society (2020) Vol.4, Issue 2: 102-107. https://doi.org/10.25236/IJNDES.040220.
 Carletti M, Burrage K, Burrage P M (2004). Numerical simulation of stochastic ordinary differential equations in biomathematical modelling [J]. Mathematics and Computers in Simulation, vol. 64, no. 2, pp. 271-277.
 Leach P G L, Andriopoulos K (2017). Application of Symmetry and Symmetry Analyses to Systems of First-Order Equations Arising from Mathematical Modelling in Epidemiology [J]. Symmetry in Nonlinear Mathematical Physics, vol. 50, no. 1, pp. 159-169.
 Ibragimov N H, Ibragimov R N (2012). Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences [J]. Mathematical Modelling of Natural Phenomena, vol. 7, no. 2, pp.52-65.
 Bonin C R B, Fernandes G C, Dos Santos R W, et al (2017). Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology [J]. Human Vaccines & Immunotherapeutics, vol.13, no. 2, pp. 484-489.
 Semenov V A, Krylov P B, Morozov S V, et al (2000). An object-oriented architecture for applications of scientific visualization and mathematical modeling [J]. Programming and Computer Software, vol.26, no.2, pp. 74-83.
 Korch M, Rauber T (2010). Storage space reduction for the solution of systems of ordinary differential equations by pipelining and overlapping of vectors [J], vol. 128, no. 1, pp. 15-26.
 Bonin, Carla Rezende Barbosa, Fernandes, Guilherme Cortes, dos Santos, Rodrigo Weber (2018). Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology [J]. Hum Vaccin Immunother, vol. 13, no. 2, pp.484-489.