The Results Comparison of Numerical and Analytical Methods for Electric Potential on Rectangular Pipes

Abstract

Two methods can be used to solve the problem of electric potential distribution in a rectangular pipe: numerical and analytical. The analytical solution is obtained using the Laplace equation and the given boundary conditions to complete the solution in the form of a linear combination of sinusoidal and hyperbolic functions. While the numerical solution is obtained using the finite difference method in the Python programming language. The comparison between the analytical and numerical solutions shows that the two have a good fit. This can be seen from the graph of the electric potential distribution in the rectangular pipe produced by the two methods. Numerical solutions obtained using the finite difference method in the Python programming language provide accurate and efficient results in solving the problem of the electric potential distribution in rectangular pipes. The use of the first four terms in the analytical method and the selection of 4 observation points on the pipe, namely points A (3.33, 1.67), B (3.33, 3.34), C (6.67, 1.67), and D (6.67, 3.34) produces a difference in the electric potential value between analytical and numerical methods each point is 35.91%, 51.96%, 51.96%, and 35.91%. The value difference between analytical and numerical methods will be smaller if more terms are taken in the analytical calculation, and more observation points are considered on the pipe.