Differential Equations

FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS

SOLUTION OF THE INITIAL VALUE PROBLEM FOR ODES

ROUTINE DESCRIPTION
IVPRK Solves an initial-value problem for ordinary differential equations using the Runge-Kutta-Verner fifth-order and sixth-order method.
IVMRK Solves an initial-value problem y’ = f(t, y) for ordinary differential equations using Runge-Kutta pairs of various orders.
IVPAG Solves an initial-value problem for ordinary differential equations using either Adams-Moulton?s or Gear?s BDF method.
 

SOLUTION OF THE BOUNDARY VALUE PROBLEM FOR ODES

ROUTINE DESCRIPTION
BVPFD Solves a (parameterized) system of differential equations with boundary conditions at two points, using a variable order, variable step size finite difference method with deferred corrections.
BVPMS Solves a (parameterized) system of differential equations with boundary conditions at two points, using a multiple-shooting method.
DAESL Solves a first order differential-algebraic system of equations, g(t, y, y’) = 0, with optional additional constraints and user-defined linear system solver.
 

FIRST-AND-SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS

SOLUTION OF THE INITIAL-VALUE PROBLEM FOR ODES

ROUTINE DESCRIPTION
IVOAM Solves an initial-value problem for a system of ordinary differential equations of order one or two using a variable order Adams method.
 

PARTIAL DIFFERENTIAL EQUATIONS

SOLUTION OF SYSTEMS OF PDES IN ONE DIMENSION

ROUTINE DESCRIPTION
PDE_1D_MG Method of lines with Variable Griddings.
MMOLCH Solves a system of partial differential equations of the form ut = f(x, t, u, ux, uxx) using the method of lines.
FEYNMAN_KAC Solves the generalized Feynman-Kac PDE on a rectangular grid using a finite element Galerkin method.
HQSVAL This rank-1 array function evaluates a Hermite quintic spline or one of its derivatives for an array of input points.
 

SOLUTION OF A PDE IN TWO AND THREE DIMENSIONS

ROUTINE DESCRIPTION
FPS2H Solves Poisson?s or Helmholtz?s equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.
FPS3H Solves Poisson?s or Helmholtz?s equation on a three-dimensional box using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.
 

STURM-LIOUVILLE PROBLEMS

ROUTINE DESCRIPTION
SLEIG Determines eigenvalues, eigenfunctions and/or spectral density functions for Sturm-Liouville problems.
SLCNT Calculates the indices of eigenvalues of a Sturm-Liouville problem.