Ordinary differential equations
| ライブラリ名 | 概要 |
|---|---|
 Runge-Kutta Method (Second-Order, First-Order Ordinary Differential Equation) | We will find the solution y = f(x) to the first-order ordinary differential equation y’ = F(x, y) using the second-order Runge-Kutta method. Given the initial condition y₀ = f(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |
| Runge-Kutta method (fourth-order, first-class ordinary differential equation) | We will solve for the solution y = f(x) of the first-order ordinary differential equation y’ = F(x, y) using the fourth-order Runge-Kutta method. Given the initial condition y₀ = f(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |
| Runge-Kutta method (second-order, second-class ordinary differential equations) | We will find the solution y = f(x) to the second-order ordinary differential equation y'' = F(x, y, y') using the second-order Runge-Kutta method. Given the initial conditions y₀ = f(x₀) and y'₀ = f'(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |
| Runge-Kutta method (fourth-order, second-class ordinary differential equation) | We will find the solution y = f(x) to the second-order ordinary differential equation y'' = F(x, y, y') using the fourth-order Runge-Kutta method. Given the initial conditions y₀ = f(x₀) and y'₀ = f'(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |
| Euler's method (first-order ordinary differential equations) | We will use Euler’s method to find the solution y = f(x) to the first-order ordinary differential equation y’ = F(x, y). Given the initial condition y₀ = f(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |
| Euler's method (second-order ordinary differential equations) | We will use the Euler method to find the solution y = f(x) to the second-order ordinary differential equation y’’ = F(x, y, y’). Given the initial conditions y₀ = f(x₀) and y’₀ = f’(x₀), we will solve for x in the range x₀ ≤ x ≤ x_n. |