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--- libnum:examples:gear [2026/03/04 14:46] – 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 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 <stdio.h>
-#include <math.h>
-#include "libnum/gear.h"
-using namespace NumericMethods;
-bool derfun1(int n, double x, const double y[], double dy[])
-{
-  dy[0] = y[1];
-  dy[1] = -y[0];
-  return true;
-}
-bool jacobian1(int n, double x, const double y[], double j[])
-{
-  j[0] = 0; j[1] = 1; j[2] = -1; j[3] = 0;
-  return true;
-}
-bool my_print1(const GearEngineContext&);
-int main()
-{
- double initValues[] = { 0, 1, 0, 0};
- GearUserProc uf1(diffun1), uf2(j1);
- Gear solver;
- solver.set(2, &uf1, &uf2); // task dimention is 2
- GearAssistant& assistant = solver.assistant;
- assistant.params.setParameter("HINI", 0.0001);  // starting step of integration
- assistant.params.setParameter("EPS", 0.001);    // step error constant
- GearEngineCallbackEmbed printHandler(my_print);
- solver.setCallback(printHandler);
- try
- {
-  Message rc=solver.solve(0, 5, initValues);     // integrate for t from 0 to 5
-  printf("\n\nsteps: %d, derCalls: %d, jacCalls: %d\n\n",
-    assistant.statistics.steps, assistant.statistics.derCalls,
-    assistant.statistics.jacCalls);
- }
- catch(Message& e)
- {
-   printf("\n\n%s",e.getMessageID().data());
- }
- printf("\n");
-}
-bool my_print1(const GearEngineContext& context)
-{
- printf("\n%10.5f:",context.t);
- // print y values and their derivatives
- int n = context.n;
- for(int i=0; i < n; ++i) printf("\t%10.5f %10.5f,",
-     context.Z[i], context.Z[i+n]/context.h);
- printf("\t(%10.5f  %d)\n", context.h, context.q);
- return true;
-}
-</file>