IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-05202-6_11.html
   My bibliography  Save this book chapter

Differential Equations

In: Introduction to Mathematics for Economics with R

Author

Listed:
  • Massimiliano Porto

    (Kobe University)

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.

Suggested Citation

  • Massimiliano Porto, 2022. "Differential Equations," Springer Books, in: Introduction to Mathematics for Economics with R, chapter 0, pages 691-799, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-05202-6_11
    DOI: 10.1007/978-3-031-05202-6_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-05202-6_11. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.