General Description:

A collection of codes for solving linear and nonlinear ordinary differential equations (ODEs).
A work in progress.

Compiling and Executing

A Makefile is provided to build the code and has been written to be compatible with Windows and Linux OS. The Makefile has been configured to use main or test as the default executable. To build the code, use:

make main.exe

By default, the code is built with double precision (real64). This can be changed within the module MOD_Select_Real_Kind.f90. After the code is built, module and executable files will be placed in a build directory. Use:

./main

to run the code with your main program.

Repository Structure

The following module files are used:

1. MOD_IO_Toolbox.f90
2. MOD_ODE_Systems.f90
3. MOD_ODE_Toolbox.f90
4. MOD_Select_Kind.f90

The primary file is MOD_ODE_Toolbox.f90. All ODE solvers and necessary helper subroutines/functions are contained here. A separate module, MOD_ODE_Systems.f90, contains examples of various ODE systems that may be useful. Using this module is not required since the ODE system may be defined in any convenient location that has access to the abstract interface shown in MOD_ODE_Toolbox.f90. A module file with data input/export subroutines, MOD_IO_Toolbox.f90, is also provided for convenience.

Methods

The code currently contains the following solvers:

• ODE_Numerical_Solve_RK4 - Implements a fixed-step classical Runge-Kutta (RK4) method for solving a system of first-order ODEs.
• ODE_Numerical_Solve_RK4_Adaptive - Adaptive RK4 solver with error control for variable step-size integration.
• ODE_Numerical_Solve_VSS - Variable Step Size (VSS) ODE solver using the Dormand-Prince RK5 method with adaptive step control for handling moderately stiff ODEs.

Detailed documentation on how to use the codes is provided in the PDF FORTRAN_ODE_Toolbox.pdf.

Future Features

1. Implicit solvers for stiff systems.
2. Boundary value solvers.