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--- libnum:examples:gear [2026/03/04 13:52] – created abc
+++ libnum:examples:gear [2026/03/29 13:46] (current) – abc
@@ Line 1: / Line 1: @@
-====== Integration of Systems of Linear Differential Equations ======
+====== Integration of Systems of Linear Differential Equations. Gear's method ======
-Gear Method.\\
 Let's examine the following //SLDE//:
-  f′
+  y₁′ = y₂
+  y₂′ = y₁
+  y₁(0)=0  and  y₂(0)=1
+NB: we expect //sin(x)/cos(x)// as the result.
 <file>
-#include <stdio.h>
+#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]] ]