Relative increase or decrease of the L_1,error of the Gresho-chan vortex at t = 1 and n_x = 64 for different kernels in respect to the L_1,error of the C₂ kernel. The terms N32, N64, N128, and N256 refer to the number of neighbors: N_smooth = 32,64,128,256. Left : simulations done with the GDSPH method. Right : simulations done with the ISPH method. The L_1,error of the C2 kernel for each N_smooth is L_1,error = 1.49375 × 10⁻¹, 9.57342 × 10⁻², 4.70888 × 10⁻², 2.99816 × 10⁻² for GDSPH and L_1,error = 9.34635 × 10⁻², 4.66192 × 10⁻², 2.64744 × 10⁻², 2.22268 × 10⁻² for ISPH. An improvement for the optimized kernel at a given N_smooth across all N_smooth can be seen for both methods, where the biggest improvements are for the N64 and N128 for GDSPH and N32 and N64 for ISPH. Of the non-optimized kernels, we observed that the C₂ kernel performs best, except for N_smooth = 32 (GDSPH), N_smooth = 32,64 (ISPH), where CM₀₅ performs better and C₄ performs slightly better at N_smooth = 256 (ISPH).