Imagine solving complex differential equations without writing a single line of code. This paper introduces a system designed to enable end-users to solve nonlinear differential equations without the need for traditional programming. The system focuses on nth order space and first-order time systems, accommodating both initial and two-point boundary value specifications. Users can input problems in direct mathematical notation, with the system automatically generating a solution graph. A key feature is the ability to computationally steer the model, allowing users to alter equations in-situ. This facilitates rapid model prototyping and experimentation. The implementation leverages an object-oriented paradigm, robust numerical procedures, and distributed computing to handle numerically intensive tasks. Ultimately, the system streamlines the process of solving differential equations, making it accessible to a broader range of users and accelerating the development of mathematical models. This approach has important implications for education, applied mathematics, and simulation-based research.
This paper, published in ACM Transactions on Mathematical Software, directly aligns with the journal's emphasis on numerical methods and software tools for mathematical problem-solving. The focus on differential equations and model prototyping is highly relevant to the journal’s audience, offering a practical system for researchers and practitioners in mathematical software development and application.