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Diffeq class
Shodor > CSERD > Resources > Libraries > Diffeq class
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Diffeq class documentation

The Diffeq class is designed to solve for the solution of a system of first order differential equations x'(x,t) = f(x,t).

Algorithms used include Euler's method, improved Euler's method, and the 4th order Runge Kutta method (from MathWorld.)

Languages:

  • C++
  • Java

    C++

    The Diffeq class is called at construction with the number of equations to be solved. The programmer sets the initial values by accessing the member variable x. The programmer provides a routine deriv that calculates the derivatives based on value of x and time.

    Member variables

    
   int neq;           //number of equations
   double *x;         //equation values at a given time
   double time;       //time variable
   double * der;      //workspace for derivative calcualtion
   double * x_old;    //workspace for equation values
   double * der_old;  //workspace for derivative calcualtion
   double * k1;       //workspace for Runge Kutta calculation
   double * k2;       //workspace for Runge Kutta calculation
   double * k3;       //workspace for Runge Kutta calculation
   double * k4;       //workspace for Runge Kutta calculation

    Methods

  • Constructor: Diffeq(int j)
  • Destructor: ~Diffeq()
  • updateEuler(double step, void deriv(int,double,double*,double*)) - calculates next values of x by Euler method, increments time step.
  • updateIEuler(double step, void deriv(int,double,double*,double*)) - calculates next values of x by improved Euler method, increments time step.
  • updateRKutta4(double step, void deriv(int,double,double*,double*)) - calculates next values of x by 4th order Runge Kutta method, increments time step.

    Java

    The Diffeq class is called at construction with the number of equations to be solved. The programmer overrides the Diffeq class, and provides a method deriv that calculates the derivatives based on values of x and t. The programmer sets the initial values by accessing the member variable x.

    Member variables

    
   int neq;           //number of equations
   double [] x;       //equation values at a given time
   double time;       //time variable
   double [] der;     //workspace for derivative calcualtion
   double [] x_old;   //workspace for equation values
   double [] der_old; //workspace for derivative calcualtion
   double [] k1;      //workspace for Runge Kutta calculation
   double [] k2;      //workspace for Runge Kutta calculation
   double [] k3;      //workspace for Runge Kutta calculation

    Methods

  • Constructor: Diffeq(int j)
  • Destructor: ~Diffeq()
  • updateEuler(double step) - calculates next values of x by Euler method, increments time step.
  • updateIEuler(double step) - calculates next values of x by improved Euler method, increments time step.
  • updateRKutta4(double step) - calculates next values of x by 4th order Runge Kutta method, increments time step.
  • deriv(int n, double time, double [] x, double [] xder) - routine to take position values as an array of doubles x and calculate derivatives stored in array of doubles xder.
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