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| """ | |
| Example usage for ODE solvers. Can be run as a script. | |
| """ | |
| import numpy as np | |
| from solve_first_order_ode import solve_first_order_ode | |
| from solve_second_order_ode import solve_second_order_ode | |
| if __name__ == '__main__': | |
| # --- First-order ODE example: dy/dt = -y*t with y(0)=1 --- | |
| def first_order_example(t, y): | |
| return -y * t | |
| print("Solving dy/dt = -y*t, y(0)=1 from t=0 to t=5") | |
| solution1 = solve_first_order_ode(first_order_example, (0, 5), [1], t_eval_count=50) | |
| if solution1['success']: | |
| print(f"First-order ODE solved. Message: {solution1['message']}") | |
| if solution1['plot_path']: | |
| print(f"Plot saved to {solution1['plot_path']}") | |
| else: | |
| print(f"First-order ODE failed. Message: {solution1['message']}") | |
| # --- First-order system example: Lotka-Volterra --- | |
| a, b, c, d = 1.5, 0.8, 0.5, 0.9 | |
| def lotka_volterra(t, y): | |
| prey, predator = y[0], y[1] | |
| d_prey_dt = a * prey - b * prey * predator | |
| d_predator_dt = c * prey * predator - d * predator | |
| return [d_prey_dt, d_predator_dt] | |
| print("\nSolving Lotka-Volterra system from t=0 to t=20 with y0=[10, 5]") | |
| solution_lv = solve_first_order_ode(lotka_volterra, (0, 20), [10, 5], t_eval_count=200) | |
| if solution_lv['success']: | |
| print(f"Lotka-Volterra solved. Plot saved to {solution_lv['plot_path']}") | |
| else: | |
| print(f"Lotka-Volterra failed. Message: {solution_lv['message']}") | |
| # --- Second-order ODE example: d²y/dt² = -sin(y) (simple pendulum) --- | |
| g_L = 9.81 / 1.0 # Example: g/L = 9.81 | |
| def pendulum_ode(t, y_angle, dy_dt_angular_velocity): | |
| return -g_L * np.sin(y_angle) | |
| print("\nSolving d²y/dt² = -g/L*sin(y), y(0)=pi/4, dy/dt(0)=0 from t=0 to t=10") | |
| solution2 = solve_second_order_ode(pendulum_ode, (0, 10), y0=np.pi/4, dy0_dt=0, t_eval_count=100) | |
| if solution2['success']: | |
| print(f"Second-order ODE solved. Message: {solution2['message']}") | |
| if solution2['plot_path']: | |
| print(f"Plot saved to {solution2['plot_path']}") | |
| else: | |
| print(f"Second-order ODE failed. Message: {solution2['message']}") | |