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Initial Value Problems

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Introduction to Scientific Computing and Data Analysis

Part of the book series: Texts in Computational Science and Engineering ((TCSE,volume 13))

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Abstract

In this chapter we derive numerical methods to solve the first-order differential equation

$$\displaystyle{ \frac{dy} {dt} = f(t,y),\;\;\text{ for }\;0 <t, }$$
(7.1)

where

$$\displaystyle{ y(0) =\alpha. }$$
(7.2)

This is known as an initial value problem (IVP), and it consists of the differential equation (7.1) along with the initial condition in (7.2). Numerical methods for solving this problem are first derived for the case of when there is one differential equation. Afterwards, the methods are extended to problems involving multiple equations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA

    Mark H. Holmes

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  1. Mark H. Holmes
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Holmes, M.H. (2016). Initial Value Problems. In: Introduction to Scientific Computing and Data Analysis. Texts in Computational Science and Engineering, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-30256-0_7

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