This discussion focuses on evaluating the convergence of Fourier series derived from solving partial differential equations (PDEs). The primary method discussed involves calculating the average error using the formula |f(n)-f(n+1)|/|f(n+1)|, where f represents the PDE function and n denotes the number of components. The goal is to determine the minimum number of terms required for convergence to be within a specified percentage, X%. The brute force approach of comparing successive terms is emphasized as an effective strategy for achieving this evaluation.
PREREQUISITESMathematicians, engineers, and researchers working with Fourier series and partial differential equations, particularly those focused on convergence evaluation and numerical analysis.
ChaseRLewis said:Well brute force is Solve with n vars then solve with n+1 vars and compare |n-(n+1)|/|n+1| once that is less than X% difference you can do that. Since each individual component should have less value towards the total solution than the previous one.