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--- libnum:examples:gear [2026/03/29 13:46] – abc
+++ libnum:examples:gear [Unknown date] (current) – removed - external edit (Unknown date) 127.0.0.1
@@ Line 1: / Line 1: @@
-====== 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>
-----
-[ [[..:classes:|Libnum methods]] ]