Efficient Numerical Evaluation of Triple Integral Using the Euler's Method and Richardson's Extrapolation

ABSTRACT In this study, we transform a triple integral into a third‐order initial value problem and solve it using Euler's method and Richardson's extrapolation. Our objective is to resolve the computational challenges associated with triple integration by reformulating it into an initial value problem. Euler's method serves as a fundamental numerical technique for approximating the solution, establishing a baseline for accuracy. We subsequently improve computational precision using Richardson's extrapolation, which systematically reduces numerical errors. This approach not only illustrates the adaptability of numerical methods in solving intricate mathematical problems, but it also emphasizes the significance of strategic error reduction techniques in enhancing computational outcomes. We demonstrate the efficacy of this method in efficiently solving triple integrals through experimentation and analysis, thereby making a significant contribution to the fields of numerical computation and mathematical modeling.