🔢 mathematics
Analytical and Gegenbauer spectral solutions of damped wave equations with singular potentials in ℝn
This paper presents a comprehensive analytical and numerical study of multi-dimensional damped wave equations with singular potentials, establishing rigorous convergence and stability results for an eigenfunction expansion solution while developing a high-order Gegenbauer collocation method that achieves algebraic convergence rates consistent with the singularity-induced regularity loss.