Finite Differences

Finite difference method example

We calculate central differences for a given function and compare it to the analytical solution.

#include <Vc/Vc>
#include <iostream>
#include <iomanip>
#include <cmath>
#include "../tsc.h"
#include <common/macros.h>

using Vc::float_v;

static constexpr std::size_t N = 10240000, PrintStep = 1000000;

static constexpr float epsilon = 1e-7f;
static constexpr float lower = 0.f;
static constexpr float upper = 40000.f;
static constexpr float h = (upper - lower) / N;

// dfu is the derivative of fu. This is really easy for sine and cosine:
static inline float  fu(float x) { return ( std::sin(x) ); }
static inline float dfu(float x) { return ( std::cos(x) ); }

static inline Vc::float_v fu(Vc::float_v::AsArg x) {
#ifdef USE_SCALAR_SINCOS
  Vc::float_v r;
  for (size_t i = 0; i < Vc::float_v::Size; ++i) {
    r[i] = std::sin(x[i]);
  }
  return r;
#else
  return Vc::sin(x);
#endif
}

static inline Vc::float_v dfu(Vc::float_v::AsArg x) {
#ifdef USE_SCALAR_SINCOS
  Vc::float_v r;
  for (size_t i = 0; i < Vc::float_v::Size; ++i) {
    r[i] = std::cos(x[i]);
  }
  return r;
#else
  return Vc::cos(x);
#endif
}

    Vc::free(dy_points - float_v::Size + 1);
    return 0;
}