Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities

We present a general method for solving the modified Helmholtz equation without shape approximation an arbitrary periodic charge distribution, whose solution is known as Yukawa potential or screened Coulomb potential. The extension of Weinert’s pseudo-charge [Weinert M, J Math Phys , 1981, 22:2433–2439] Poisson same class density distributions. inherent differences between and are in their respective radial solutions. These polynomial functions, equation, spherical Bessel equation. This leads to definition multipole moments. have shown that convergence analysis absolutely uniformly convergent Fourier series transferred density. conclude by illustrating algorithmic changes necessary turn available implementation solver into