int main(int argc, char **argv)
{
int i, N = 100; /* Number of nodes (discretization) */
double t0 = 0.0, y0 = 0.5; /* Initial conditions */
double h = 1.0/N; /* RK step */
double time, y; /* y (solution) at time - time */
FILE *fp;
/* Open a file to write in the results */
/* One can store the results in vectors */
fp = fopen( "results.dat", "w" );
for(i = 0; i < N; i++){
eulerStep(f,t0,y0,h,i,&time,&y);
/* rkFehlbergStep(f, fy, t0, y0, h, i, &time, &y); */
fprintf( fp, "%f %f\n", time, y );
t0 = time;
y0 = y;
}
fclose(fp);
return 0;
}
/*
* 打印通过欧拉法
*/
void eulerPrint(OdeFormula f,real t0,real x0,real step,int n)
{
real t,x,h;
t = t0;
x = x0;
h = step;
printf("euler method,initial value t=%.4f x=%.4f step=%.4f\n",t0,x0,step);
printf("%.4f\t|%.4f\n",t,x);
for(int i=0;i<n;i++){
x = eulerStep(f,t,x,h);
t+=h;
printf("%.4f\t|%.4f\n",t,x);
}
}
/*
* This is an entry point to the time integration. When things are fully
* running we do a third level Adams-Bashforth scheme which requires knowing the
* past three forcing evaluations. Since these are not available intitially,
* the first few steps are lower order while we ramp up.
*/
void step()
{
if(iteration == 1)
{
eulerStep();
}
else if(iteration == 2)
{
AB2Step();
}
else
{
AB3Step();
}
elapsedTime += dt;
}
/*
* 对三种方法比较进行比较
*/
void comparePrint(OdeFormula f,real t0,real x0,real step,int n)
{
real t,x,h,mx,sx,A,tx;
t = t0;
tx = sx = mx=x = x0;
h = step;
A = f(t,x,INITIAL);
printf("变量\t|欧拉法\t误差\t|中点法\t误差\t误差比\t|测试\t误差|公式法|\n");
for(int i=0;i<n;i++){
x = eulerStep(f,t,x,h);
mx = midpointStep(f,t,mx,h);
tx = testStep(f,t,tx,h);
t+=h;
sx = f(t,A,SOLVE);
printf("%.4f\t|%.4f\t%.4f\t|%.4f\t%.4f\t%.4f\t|%.4f\t%.7f|%.4f|\n",t,x,sx-x,mx,mx-sx,fabs(mx-sx)/fabs(sx-x),tx,tx-sx,sx);
}
}
// Simulation step using interpolation
void Sim::simStep()
{
int type = 2;
float dt = 0.1f;
t += dt;
switch (type)
{
case 0:
rightStep();
break;
case 1:
eulerStep(dt);
break;
case 2:
semiImplicitEuler(dt);
break;
default:
rungeKuttaStep(dt); // This fails after multiple collisions!
}
}