NMath User's Guide

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35.2 Solving Differential Equations (.NET, C#, CSharp, VB, Visual Basic, F#)

Class RungeKuttaSolver solves first order initial value differential equations by the Runge-Kutta method. The solver computes the unknown function y as set of tabulated values such that .

Constructing RungeKuttaSolver Instances

Instances of RungeKuttaSolver are constructed from the number of tabulated points and a nonzero value delta. From the number of points and the delta, the set is determined as .

For instance:

Code Example – C# ordinary differential equations (ODE)

int n = 2000;

double delta = .001;

var solver = new RungeKuttaSolver( n, delta );

Code Example – VB ordinary differential equations (ODE)

Dim N As Integer = 2000

Dim Delta As Double = 0.001

Dim Solver As New RungeKuttaSolver(N, Delta)

Optionally, the order of the Runge-Kutta method may also be specified, using the enum RungeKutterSolver.SolverOrder.

Code Example – C# ordinary differential equations (ODE)

var solver = new RungeKuttaSolver( n, delta, SolverOrder.First );

Code Example – VB ordinary differential equations (ODE)

Dim Solver As New RungeKuttaSolver(N, Delta, SolverOrder.First)

By default, the fourth order Runge-Kutta method (RK4) is used.

Solving First Order Initial Value Problems

The Solve() method on RungeKuttaSolver solves a given FirstOrderInitialValueProblem by the common Runge-Kutta method. The Solve() method computes the unknown function y as set of tabulated values such that . The tabulated values are returned either as a KeyValuePair<double[], double[]>, or as a CenterSpace.NMath.Core.TabulatedFunction passed by reference. (See Section 13.5 for more information on tabulated functions.)

For example:

Code Example – C# ordinary differential equations (ODE)

KeyValuePair<double[], double[]> tabulatedValues =

  solver.Solve( prob );

Code Example – VB ordinary differential equations (ODE)

Dim TabulatedValues As KeyValuePair(Of Double(), Double()) = 

  Solver.Solve(Prob)

or

Code Example – C# ordinary differential equations (ODE)

TabulatedFunction ftab = null;

solver.Solve( prob, ref ftab );

Code Example – VB ordinary differential equations (ODE)

Dim FTab As TabulatedFunction = Nothing

Solver.Solve(Prob, FTab)

Similarly, in the following code, results are returned as a LinearSpline, a subclass of TabulatedFunction that provides linear interpolation between tabulated values:

Code Example – C# ordinary differential equations (ODE)

var spline = new LinearSpline();

solver.Solve( prob, ref spline );

Code Example – VB ordinary differential equations (ODE)

Dim Spline As New LinearSpline()

Solver.Solve(Prob, Spline)

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