Numerical Analysis of Distance Estimation and Convergence Using Newton's Forward Interpolation with an Interactive Application

Accurate distance estimation based on time data is crucial in industries such as logistics, engineering, and academic research. However, current methods often fail to provide efficient and precise models, relying instead on time-consuming manual calculations or simplistic approximations. This project proposes the development of an application that allows users to input discrete time and distance data points and derive a mathematical distance function using Newton's Forward Divided Difference Interpolation Method. The application will enable users to estimate distances at any specified time accurately, addressing critical inefficiencies in traditional interpolation techniques. To test the accuracy of the application, convergence analysis will be performed by gradually increasing the number of data points (using time and distance data from the MRT Kajang line). This analysis will allow the user to observe how the estimation error reduces with more data, demonstrating the improvement in accuracy as the dataset grows. The solution simplifies complex mathematical processes, reduces calculation errors, and enhances productivity across technical and analytical workflows. Its user-friendly interface ensures accessibility for professionals, researchers, and students alike. The application holds strong commercialization potential, as it can be deployed in fields such as transportation planning, scientific modeling, and educational tools for teaching numerical methods. By offering a reliable, scalable, and efficient distance estimation solution, this application addresses a pressing need in data analysis and predictive modeling, paving the way for smarter decision-making and improved operational efficiency in various sectors.