Table of Contents

Explicit Euler Method

Routine Name: explicit_euler

Author: Philip Nelson

Language: C++

Description

explicit_euler is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. 1

Input

explicit_euler(T x0, T y0, T x, T dt, F f) requires:

• T x0 - the initial x
• T y0 - the initial y
• T x - the value of x for which you want to find value of y
• T dt - the delta t step
• F f - the function defining \(\frac{dy}{dx}\)

Output

The value of y at x.

Code

template <typename T, typename F>
T explicit_euler(T x0, T y0, T x, T dt, F f)
{
  auto tol = maceps<T>().maceps;
  while (std::abs(x - x0) > tol)
  {
    y0 = y0 + (dt * f(x0, y0));
    x0 += dt;
  }
  return y0;
}

Example

int main()
{
  std::cout <<
    explicit_euler(0.0, -1.0, 0.4, 0.1, [](double a, double b){return a*a+2*b;})
    << std::endl;
}

Result

-2.05836

Last Modification date: 21 March 2018