Common Lisp numerical ordinary differential equation solvers
Common Lisp
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Failed to load latest commit information.


Ordinary differential equations solvers in Common Lisp Currently includes adaptive stepsize Runge-Kutta method. Define a function of independant variable & state object as the differential equation to solve. State may be any object with generic arithmetic methods for addition, subtraction, and multiplication by a scalar number defined. Number, vector, and hash table state methods are provided. An infinity norm method is also required, which is defined in the generic function NORMINFX.


(rka fun t0 tf x0 :a *a-dp* :bl *bl-dp* :bh *bh-dp* :c *c-dp* :tol 1d-6 :hmax 0.25 :h0 (/ (- tf t0) 200d0) :hmin (/ (- tf t0) 1d12) :param parameter)


  • FUN: function of independant variable & state, e.g. (fun tn x)
  • T0: starting independant variable
  • TF: final independant variable
  • X0: state at T0

Optional keyword arguments

  • :A - A matrix (default Dormand-Prince)
  • :BL - lower order B vector (default Dormand-Prince)
  • :BH - higher order B vector (default Dormand-Prince)
  • :C - C vector (default Dormand-Prince)
  • :TOL - relative tolerance
  • :HMAX - max stepsize
  • :H0 - initial stepsize
  • :HMIN - minimum stepsize
  • :PARAM - parameter to pass to ODE function


Integrate (cos (* p tn)) over tn range 0 to 2pi where p = 2:

(defun testfun (tn x &optional p)	
  (cos (* p tn)))
(rka #'testfun 0d0 (* 2d0 pi) 0d0 :param 2)

Custom State Classes

Vector and hash tables are provided as state types you can use. If you define a custom class as a state, the macro DEFSTATEARITHMETIC can be used to define methods on your class for the state arithemetic used in BLD-ODE. If your :INITARG entries are different from the slot names, you can define them - in the same order as SLOTS - using the keyword argument :INITARGS

You can choose which slots of your class to use in the state algebra, leaving some out to serve other purposes.


(defclass state ()
   ((x :initarg :x)
    (dx :initarg :dx)))
(defstatearithmetic state (x dx))

Optionally specify the INITARG entries:

(defclass state ()
   ((x :initarg :xarg)
    (dx :initarg :dxarg)))
(defstatearithmetic state (x dx) :initargs (:xarg :dxarg))

Also, you can specify data slots that are simply copied and not used in integration:

(defclass state ()
   ((x :initarg :x)
    (dx :initarg :dx)
(defstatearithmetic state (x dx) :oslots (data1 data2))