Ordinary Differential Equations

Ordinary differential equations (ODEs) pervade geosciences. When studying long-term behavior of earth, box models are used which are described by a set of ODEs. ODEs also occur when using system’s thinking about earth. Also, when focus is on steady state and one space-dimensional problem, again ODEs are used. Further, numerical solutions of PDEs often are obtained by decomposing them into a set of coupled ODEs. Both initial and boundary value problems for ODEs have been developed along with eigenvalue/eigenvectors and Green’s function method. For variable coefficients, some solutions are written in terms of special functions, or recourse to numerical methods is taken using powerful computer programs like highly popular Python’s odeint() method. This entry has described the ODEs as applicable to the earth problems.