Initial Value Problems


Before we discuss how to solve them, let's explore a little bit about the nature of ODEs themselves . There are two basic types of boundary condition categories for ODEs ”initial value problems and two-point boundary value problems. With an initial value problem, values for all of the dependent variables are specified at the beginning of the range of integration. The initial boundary serves as the "anchor" for the solution. The solution is marched outward from the initial boundary by integrating the ODE at discrete steps of the independent variable. The dependent variables are computed at every step.

Initial value problems are simpler to solve because you only have to integrate the ODE one time. The solution of a two-point boundary value problem usually involves iterating between the values at the beginning and end of the range of integration. The most commonly used techniques to solve initial value problem ODEs are called Runge-Kutta schemes and will be discussed in the next section.



Technical Java. Applications for Science and Engineering
Technical Java: Applications for Science and Engineering
ISBN: 0131018159
EAN: 2147483647
Year: 2003
Pages: 281
Authors: Grant Palmer

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