May 2020
Intermediate to advanced
656 pages
16h 6m
English
book
Applied Numerical Methods Using MATLAB, 2nd Edition
by Won Y. Yang, Wenwu Cao, Jaekwon Kim, Kyung W. Park, Ho-Hyun Park, Jingon Joung, Jong-Suk Ro, Han L. Lee, Cheol-Ho Hong, Taeho Im
Content preview from Applied Numerical Methods Using MATLAB, 2nd Edition
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6Ordinary Differential Equations
Chapter Outline
Differential equations (DEs) are mathematical descriptions of how the variables and their derivatives (rates of change) with respect to one or more independent variable affect each other in a dynamical way. Their solutions show us how the dependent variable(s) will change with the independent variable(s). Many problems in natural sciences and engineering fields are formulated into a scalar differential equation or a vector differential equation, i.e. a system of differential equations.
In this chapter, we look into several methods of obtaining the numerical solutions to ordinary differential equations (ODEs) in which all dependent variables (x) depend on a single independent variable (t). First, the initial value problems (IVPs) will be handled with several methods including Runge‐Kutta method and predictor‐corrector methods in Sections 6.1 to 6.5. The last section (Section 6.6) will introduce the shooting method and the finite difference method for solving ...
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