# Ordinary Differential Equations

## Abstract

An ordinary differential equation (ODE) involves the derivatives of an unknown function that is dependent on a single independent variable. Its solution is usually constructed subject to a set of constraints referred to as initial or boundary conditions. Therefore, the ODEs are classified as initial value problems (IVP) and boundary value problems (BVP). In the case of a nonlinear ODE, the solution to its corresponding discrete form as nonlinear system of algebraic equations is achieved by using the Newton-Raphson method. The initial guess for the solution may be set to zero. The solution procedure is repeated until the relative error becomes less than the desired tolerance which is specified as *ε* = 10^{−5} throughout this chapter.

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