====== Integration of Systems of Linear Differential Equations. Gear's method ======

Let's examine the following //SLDE//:
  y₁′ = y₂
  y₂′ = y₁
  y₁(0)=0  and  y₂(0)=1
NB: we expect //sin(x)/cos(x)// as the result.

<file>
#include <iostream>
#include <sstream>
#include <fstream>

#include <math.h>
#include "libnum/gear.h"
#include "libnum/gear.output.h"

using namespace NumericMethods;

/*
    y₁′ = y₂
    y₂′ = y₁
    y₁(0)=0  and  y₂(0)=1
    // NB: we expect sin(x)/cos(x) as the result.
*/

static bool derfun(int n, double x, const double y[], double dy[])
{
  dy[0] = y[1];
  dy[1] = -y[0];
  return true;
}

static bool jacobian(int n, double x, const double y[], double j[])
{
  //for (int i = 0; i<n*n; ++i) j[i] = 0;
  j[0] = 0; j[1] = 1; j[2] = -1; j[3] = 0; // sin/cos
  return true;
}


int main()
{

 double initValues[]={ 0,1,0,0};
 GearUserProc uf1(derfun),uf2(jacobian);

 Gear solver;
 solver.set(2,&uf1,&uf2);
 GearAssistant& assistant = solver.assistant;
 assistant.params.setParameter("HINI", 0.000001);  // starting step of integration 
 assistant.params.setParameter("EPS", 0.0001);     // step error constant 

 //    Output variants
 /*1*/ GearPrintToStream print_1(std::cout, "{:8.5f}\t");

 /*2*/ std::stringstream buf;  // to string; use buf.str() later
 GearPrintToStream print_2(buf, "{:8.5f}\t");

 /*3*/ std::ofstream file("gear_output.txt");
 GearPrintToStream print_3(file, "{:8.5f}\t");

 GearPrintTable print_4(std::cout, 0.1);
  print_4.setFormat("{:8.5f}\t");

 solver.setCallback(print_4);

 try
 {
  Message rc=solver.solve(0, 5, initValues);
 }
 catch(Message& e)
 {
   std::cout << "\n\n" << e.getMessageID().data();
 }
 std::cout << "\n";
}
</file>

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[ [[..:classes:|Libnum methods]] ]