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"""
Solves a single second-order ordinary differential equation of the form
d²y/dt² = f(t, y, dy/dt) with initial conditions y(t0)=y0 and dy/dt(t0)=dy0_dt.
"""
import numpy as np
from scipy.integrate import solve_ivp
from typing import Callable, List, Tuple, Dict, Any, Union
import matplotlib.pyplot as plt
from maths.differential_equations.ode_interface_utils import parse_float_list, parse_time_span, string_to_ode_func
import gradio as gr
def solve_second_order_ode(
ode_func_second_order: Callable[[float, float, float], float],
t_span: Tuple[float, float],
y0: float,
dy0_dt: float,
t_eval_count: int = 100,
method: str = 'RK45',
**kwargs: Any
) -> Dict[str, Union[np.ndarray, str, bool]]:
# ...existing code...
def system_func(t: float, z: np.ndarray) -> List[float]:
y_val, dy_dt_val = z[0], z[1]
d2y_dt2_val = ode_func_second_order(t, y_val, dy_dt_val)
return [dy_dt_val, d2y_dt2_val]
initial_conditions_system = [y0, dy0_dt]
try:
t_eval = np.linspace(t_span[0], t_span[1], t_eval_count)
sol = solve_ivp(system_func, t_span, initial_conditions_system, method=method, t_eval=t_eval, **kwargs)
plot_path = None
if sol.success:
try:
plt.figure(figsize=(12, 7))
plt.subplot(2,1,1)
plt.plot(sol.t, sol.y[0], label=f'y(t), y0={y0}')
plt.xlabel("Time (t)")
plt.ylabel("y(t)")
plt.title(f"Solution of Second-Order ODE: y(t) ({method})")
plt.legend()
plt.grid(True)
plt.subplot(2,1,2)
plt.plot(sol.t, sol.y[1], label=f'dy/dt(t), dy0/dt={dy0_dt}', color='orange')
plt.xlabel("Time (t)")
plt.ylabel("dy/dt(t)")
plt.title(f"Solution of Second-Order ODE: dy/dt(t) ({method})")
plt.legend()
plt.grid(True)
plt.tight_layout()
plot_path = "ode_second_order_solution_plot.png"
plt.savefig(plot_path)
plt.close()
except Exception as e_plot:
print(f"Warning: Could not generate plot: {e_plot}")
plot_path = None
return {
't': sol.t,
'y': sol.y[0], # First component of the system's solution
'dy_dt': sol.y[1], # Second component of the system's solution
'message': sol.message,
'success': sol.success,
'plot_path': plot_path
}
except Exception as e:
return {
't': np.array([]),
'y': np.array([]),
'dy_dt': np.array([]),
'message': f"Error during ODE solving: {str(e)}",
'success': False,
'plot_path': None
}
# --- Gradio Interface for Second-Order ODEs ---
second_order_ode_interface = gr.Interface(
fn=lambda ode_str, t_span_str, y0_val_str, dy0_dt_val_str, t_eval_count, method: solve_second_order_ode(
string_to_ode_func(ode_str, ('t', 'y', 'dy_dt')),
parse_time_span(t_span_str),
parse_float_list(y0_val_str, expected_len=1)[0],
parse_float_list(dy0_dt_val_str, expected_len=1)[0],
int(t_eval_count),
method
),
inputs=[
gr.Textbox(label="ODE Function (lambda t, y, dy_dt: ...)",
placeholder="e.g., lambda t, y, dy_dt: -0.1*dy_dt - math.sin(y)",
info="Define d²y/dt². `y` is current value, `dy_dt` is current first derivative."),
gr.Textbox(label="Time Span (t_start, t_end)", placeholder="e.g., 0,20"),
gr.Textbox(label="Initial y(t_start)", placeholder="e.g., 1.0"),
gr.Textbox(label="Initial dy/dt(t_start)", placeholder="e.g., 0.0"),
gr.Slider(minimum=10, maximum=1000, value=100, step=10, label="Evaluation Points Count"),
gr.Radio(choices=['RK45', 'LSODA', 'BDF', 'RK23', 'DOP853'], value='RK45', label="Solver Method")
],
outputs=[
gr.Image(label="Solution Plot (y(t) and dy/dt(t))", type="filepath", show_label=True, visible=lambda res: res['success'] and res['plot_path'] is not None),
gr.Textbox(label="Solver Message"),
gr.Textbox(label="Success Status"),
gr.JSON(label="Raw Data (t, y, dy_dt values)", visible=lambda res: res['success'])
],
title="Second-Order ODE Solver",
description="""
Solves d²y/dt² = f(t, y, dy/dt) for a single second-order ODE.
- Enter a Python lambda for the ODE (e.g., `lambda t, y, dy_dt: -0.1*dy_dt - math.sin(y)`).
- Initial y(t_start) and dy/dt(t_start) must be single values.
**Examples:**
- Damped oscillator: `lambda t, y, dy_dt: -0.1*dy_dt - y`, y0: `1.0`, dy0/dt: `0.0`, t_span: `0,20`
- Simple pendulum: `lambda t, y, dy_dt: -9.81/1.0 * math.sin(y)`, y0: `math.pi/4`, dy0/dt: `0`, t_span: `0,10`
WARNING: Uses eval() for the ODE function string - potential security risk.
""",
flagging_mode="manual"
)
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