In many sciences, especially the science of geometric geodesy, we face problems that cannot be solved by analytical methods, or it is very difficult and impossible to solve such problems with analytical methods.
Such problems include solving integrals, ordinary differential equations with the initial value (ODE), or calculating the numerical derivative of some functions. For this purpose, the use of numerical methods is considered.
In this research project, the goal of solving the integral is to calculate the perimeter of the ellipse. To solve this integral, we first convert it into a differential equation and convert it into an initial value problem (IVP).
After preparing the initial value problem using numerical methods, we proceed to solve the desired equation and obtain the set of points that are calculated as the best approximation using numerical methods.
In this project, we will use the following three methods to numerically solve the problem of finding the perimeter of Earth’s ellipsoid:
- Euler’s method
- Heun’s method
- 4th order Runge-Kutta method
You can see the full paper in the following link: