Differential Equations

Massimiliano Porto
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Massimiliano Porto: Kobe University

Chapter Chapter 11 in Introduction to Mathematics for Economics with R, 2022, pp 691-799 from Springer

Abstract: Abstract This chapter starts by discussing the solution to differential equations, including the initial value problem (Sect. 11.1.5) and numerical solutions (Sect. 11.1.6). In the case of numerical solutions of differential equations, we cover two algorithms, the Euler method (Sect. 11.1.6.1) and the Runge-Kutta method (Sect. 11.1.6.2). Then, we will present the methods to solve first-order differential equations such as separation of variables, substitution method for homogeneous-type equations, integrating factor, exact equations, and Bernoulli equations (Sect. 11.2). The remaining part of the chapter is devoted to second-order linear differential equations (Sect. 11.4) and systems of linear differential equations (Sect. 11.5). Examples of applications in Economics include: a problem with interest rate, the advertising model, the Harrod-Domar growth model, and the Solow growth model. Examples of functions coded from scratch include: functions that solve numerically differential equations with the Euler and Runge-Kutta methods.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05202-6_11

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DOI: 10.1007/978-3-031-05202-6_11

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