Chapter 10. Ordinary Differential Equations
10.1 Introduction
10.2 Initial-Value Problem for First-Order ODE
10.3 Taylor Series Method
10.4 Runge-Kutta of Order 2 Method
10.5 Runge-Kutta of Order 4 Method
10.6 Predictor-Corrector Multistep Method
10.7 System of First-Order ODEs
10.8 Second-Order ODE
10.9 Initial-Value Problem for Second-Order ODE
10.10 Finite-Difference Method for Second-Order ODE
10.11 Differentiated Boundary Conditions
10.12 Visual Solution: Code10
10.13 Summary
Numerical Exercises
Programming Challenges
INTRODUCTION
Problems involving the ordinary differential equation (ODE) arise in many areas, including engineering, natural sciences, medicine, economics, and anthropology. These problems are normally generally numeric-intensive and require fast computers in their implementation. Solutions to these problems are normally formulated as models that involve ordinary and partial differential equations. A mathematical model is the general solution to a given problem that is subject to some conditions and limitations. A typical model works best when all conditions and constraints in the problem are satisfied. At the same time, the model may not work if one or more of these conditions are not satisfied.
An ordinary differential equation is an equation that has one or more terms in the expression in the form of derivatives. A good understanding of problems involving ordinary differential equations is necessary in order to produce efficient mathematical models and their simulations on ...
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