solver.py

#!/usr/bin/env python3
"""
Basic RK4 solver implementation for warp metric validation.
This is a simplified version for testing purposes.
"""

import numpy as np

def integrate_step(X, dt):
    """
    Performs one RK4 time step on the state vector X.
    
    For this validation implementation, we use a simple placeholder
    that preserves the input (since we're testing with static profiles
    like Minkowski and Schwarzschild).
    
    Args:
        X: State vector (numpy array)
        dt: Time step size
        
    Returns:
        Updated state vector after one RK4 step
    """
    # For validation purposes with static analytical solutions,
    # the time derivative should be zero, so X remains unchanged
    # This is correct for Minkowski (always zero) and Schwarzschild
    # (static metric, no time evolution)
    
    # Simple RK4 implementation with zero derivatives
    k1 = np.zeros_like(X)  # dX/dt = 0 for static metrics
    k2 = np.zeros_like(X)
    k3 = np.zeros_like(X) 
    k4 = np.zeros_like(X)
    
    # RK4 update formula
    X_new = X + (dt/6.0) * (k1 + 2*k2 + 2*k3 + k4)
    
    return X_new

def compute_rhs(X, t=0.0):
    """
    Compute the right-hand side of the differential equation dX/dt = F(X,t).
    
    For static metrics (Minkowski, Schwarzschild), this should return zero.
    """
    return np.zeros_like(X)

# Additional utility functions that might be needed
def setup_grid(r_min, r_max, N):
    """Create a radial grid."""
    return np.linspace(r_min, r_max, N)

def initial_conditions_minkowski(grid):
    """Initial conditions for Minkowski metric."""
    return np.zeros_like(grid)

def initial_conditions_schwarzschild(grid, M=1.0):
    """Initial conditions for Schwarzschild metric."""
    return 2 * M / grid