numerical_methods.integration package¶
Submodules¶
numerical_methods.integration.euler_methods module¶
- numerical_methods.integration.euler_methods.euler_method(f, x_end, x0, y0, h, n, f_exact)[source]¶
Solve a differential equation using the Euler method.
- Parameters:
f (Callable) – The function f(x, y) representing dy/dx.
x_end (float) – The endpoint of the interval.
x0 (float) – The initial x value.
y0 (float) – The initial y value.
h (float) – Step size (will be recomputed from x0 to x_end and n).
n (int) – Number of steps.
f_exact (Callable) – The exact solution function for comparison.
- Return type:
None
- numerical_methods.integration.euler_methods.modified_euler(f, x_end, x0, y0, h, n, f_exact)[source]¶
Solve a differential equation using Modified Euler (RK2) method.
- Parameters:
f (Callable) – Function f(x, y).
x_end (float) – End x value.
x0 (float) – Initial x.
y0 (float) – Initial y.
h (float) – Step size.
n (int) – Number of steps.
f_exact (Callable) – Exact solution.
- Returns:
Final y value.
- Return type:
float
numerical_methods.integration.midpoint_method module¶
- numerical_methods.integration.midpoint_method.midpoint_method(f, x_end, x0, y0, h, n, f_exact)[source]¶
Solve a differential equation using Midpoint method (RK2).
- Parameters:
f (Callable) – Function f(x, y).
x_end (float) – Final x value.
x0 (float) – Initial x value.
y0 (float) – Initial y value.
h (float) – Step size.
n (int) – Number of steps.
f_exact (Callable) – Exact solution.
- Returns:
Final y value at x_end.
- Return type:
float
numerical_methods.integration.runge_kutta_methods module¶
numerical_methods.integration.taylor_method module¶
- numerical_methods.integration.taylor_method.taylor_method(f, x_end, x0, y0, h, n, df_dx, df_dy, f_exact)[source]¶
Solve a differential equation using Taylor method (2nd order).
- Parameters:
f (Callable) – Function f(x, y).
x_end (float) – Endpoint of the integration interval.
x0 (float) – Initial x.
y0 (float) – Initial y.
h (float) – Step size (recalculated from interval).
n (int) – Number of steps.
df_dx (Callable) – Partial derivative of f with respect to x.
df_dy (Callable) – Partial derivative of f with respect to y.
f_exact (Callable) – Exact solution for comparison.
- Return type:
None