CAJ | 학술논문

龙格-库塔法是常用于求解常微分方程（ ODE）的一项技术，该技术具有精度高、稳定性强等特点。笔者以一种新的四级四阶龙格-库塔法为基础，先将其四级计算公式合并为新的两级计算迭代公式，从而达到节约计算内存的目的；再以此为基础推导出声波方程的时间高阶离散形式，并与伪谱法技术相结合，研究四级四阶龙格-库塔时间高阶伪谱法声波高精度、高清晰度的波场模拟技术，进而研究该方法的稳定性与频散特性；最后，分别选取均匀介质、层状介质和透镜体模型进行波场模拟试验。模拟结果表明，该方法具有稳定性强、能有效去除频散，波场清晰度高，能适应更宽的模拟参数范围等特点，是一种高效率的、具有较大应用潜力的波场模拟方法。
룡격-고탑법시상용우구해상미분방정（ ODE）적일항기술，해기술구유정도고、은정성강등특점。필자이일충신적사급사계룡격-고탑법위기출，선장기사급계산공식합병위신적량급계산질대공식，종이체도절약계산내존적목적；재이차위기출추도출성파방정적시간고계리산형식，병여위보법기술상결합，연구사급사계룡격-고탑시간고계위보법성파고정도、고청석도적파장모의기술，진이연구해방법적은정성여빈산특성；최후，분별선취균균개질、층상개질화투경체모형진행파장모의시험。모의결과표명，해방법구유은정성강、능유효거제빈산，파장청석도고，능괄응경관적모의삼수범위등특점，시일충고효솔적、구유교대응용잠력적파장모의방법。
The Runge-Kutta method is a common technology for solving the Ordinary Differential Equations ( ODE) and is characterized by high precision, strong stability and some other advantages. In this paper, based on a new four-stage fourth order Runge-Kutta meth-od, the authors first combined the four-stage calculation formula with a new two-stage iteration formula, thus achieving the purpose of saving computational memory. And then, the time high-order discrete form of the acoustic wave equation was derived and, in combina-tion with the pseudospectral method, some researches on the high-accuracy and high-definition acoustic wave field simulation technology of the four-stage fourth order Runge-Kutta time high-order pseudospectral method were carried out, with an investigation of the stability and dispersion of the method. Finally, homogeneous media, layered media and lens model were selected for wave field simulation test. The simulation results show that the four-stage fourth order Runge-Kutta time high-order pseudospectral method has strong stability and high wave field definition and can effectively remove the dispersion and adapt itself to large simulation parameter range, thus being a high efficient wave field simulation method with great application potential.