Systematic matrix formulation for efficient computational path integration

• A novel step matrix multiplication-based path integration (SMM-PI) method is created. Probability density function evolution of stochastic systems are computed. The SMM-PI gives accurate approximations very efficiently. order magnitudes faster and more reliable than similar methods. modular construction facilitates evaluation adaptation for larger systems. In this work we introduce a methodological treatment the numerical method, used computing response probability dynamical greatly accelerated by transforming corresponding Chapman-Kolmogorov equation to multiplication. With systematic formulation split solution into three separate parts: interpolate function, approximate transitional process evaluate integral in equation. We provide thorough error efficiency analysis through experiments on one, two, four dimensional problem. By comparing results obtained Path Integration with analytical solutions previous formulations demonstrate superior ability results. Potential bottlenecks identified discussion provided how address them.