Study on the calculation method of the KZK equation for parametric array

Runge-Kutta method, which does not need to calculate the higher-order derivative, can achieve the accuracy of the Taylor series expansion method. and is widely used in engineering because it is a high precision algorithm in single step. When using the KZK equation for the acoustic characteristic of parametric array, the acoustic near-field varied quickly. This paper used the second-order, diagonally-implicit Runge Kutta (DIRK2) finite difference method to solve the parametric array near-field characteristics of the pressure amplitude of the primary wave and the difference wave to reduce error and improve the accuracy of calculation, comparing to the results of the implicit finite difference (IBFD) calculation, the numerical results showed that the DIRK2 method can effectively improve the calculation accuracy, and reduce the calculation method-error of the pressure amplitude of the parametric array near-field characteristics, and reduce the acoustic axial cumulative error of the parametric array in the propagation.