👉 The word "RungeKutta4" refers to a set of mathematical methods for numerical integration that can be used in various scientific disciplines, including physics, engineering, and finance.
The main definition involves four different types of Runge-Kutta schemes: 4th order Runge-Kutta, 5th order Runge-Kutta, 6th order Runge-Kutta, and 7th order Runge-Kutta. Each type of Runge-Kutta method uses a different set of error terms to improve accuracy over time.
Each scheme includes the following components:
1.
Step Size:
The step size at each step in the integration interval.
2.
Number of Points:
The number of points used to calculate an integration value during a single iteration.
3.
Order of Error Term:
Determines how many error terms are included in each step, from first order to seventh order.
4.
Initial Condition:
Represents the initial values at the start of the integration interval.
The Runge-Kutta methods are widely used for solving differential equations and numerical solutions of partial differential equations (PDEs) in various scientific fields.
For example, one common application is in financial modeling, where it’s used to solve ODEs that describe the behavior of financial markets over time.
RungeKutta4.conf