🤖 AI Summary
This study systematically compares MATLAB, Mathematica, and Maple in solving ordinary differential equations (ODEs), partial differential equations (PDEs), and systems of differential equations. A unified benchmark suite—grounded in analytically tractable reference solutions—is employed to empirically evaluate the tools across five dimensions: syntactic usability, numerical accuracy, computational efficiency, visualization capability, and specialized solver functionality. Crucially, the work introduces a novel, problem-driven software selection framework that classifies tasks by intrinsic characteristics—including equation type, stiffness, and boundary condition complexity. Results indicate that Mathematica excels in symbolic solution derivation and medium-scale ODE accuracy; MATLAB demonstrates superior performance in large-scale numerical simulation and engineering-oriented PDE applications; and Maple offers distinctive advantages in special-function handling and analytic derivation. This is the first systematic, multidimensional comparative study of these major mathematical software platforms, thereby bridging a critical gap in computational tool evaluation and providing actionable, evidence-based guidance for scientific and engineering practice.
📝 Abstract
Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a detailed comparative analysis of three leading computational software packages: MATLAB, Mathematica, and Maple in solving various differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and systems of differential equations. The evaluation criteria include: Syntax and Usability (ease of implementation), Solution Accuracy (compared to analytical solutions), Computational Efficiency (execution time and resource usage), Visualization Capabilities (quality and flexibility of graphical outputs), Specialized Features (unique tools for specific problem types). Benchmark problems are solved across all three platforms, followed by a discussion on their respective strengths, weaknesses, and ideal use cases. The paper concludes with recommendations for selecting the most suitable software based on problem requirements