Chapter 5: Differential Equations

Routines

First-Order Ordinary Differential Equations

5.1.1     Solution of the Initial-Value Problem for ODEs

Runge-Kutta method.............................................................................................. IVPRK

Runge-Kutta method, various orders....................................................................... IVMRK

Adams or Gear method......................................................................................... IVPAG

Solution of the Boundary-Value Problem for ODEs

Finite-difference method........................................................................................ BVPFD

Multiple-shooting method..................................................................................... BVPMS

Solution of the Differential-Algebraic Systems

Solves a first order differential-algebraic system
of equations......................................................................................................... DAESL

First-and-Second-Order Ordinary Differential Equations

Solution of the  Initial-Value Problem for ODEs

Solves an initial-value problem for a system of ODEs
using a variable order Adams method .................................................................... IVOAM

Partial Differential Equations

Solution of Systems of PDEs in One Dimension

Method of lines with Variable Griddings......................................................... PDE_1D_MG

Method of lines with a Hermite cubic basis.......................................................... MMOLCH

Solves a generalized Feynman-Kac equation on a
finite interval using Hermite quintic splines................................................ FEYNMAN_KAC

Computes the value of a Hermite quintic spline or the
value of one of its derivatives
............................................................................... HQSVAL

Solution of a PDE in Two and Three Dimensions

Two-dimensional fast Poisson solver...................................................................... FPS2H

Three-dimensional fast Poisson solver.................................................................... FPS3H

Sturm-Liouville Problems

Eigenvalues, eigenfunctions,
and spectral density functions................................................................................ SLEIG

Indices of eigenvalues........................................................................................... SLCNT



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