CAJ | 학술논문

非线性计算稳定性是计算数学、计算物理、计算气象等学科中的一个重要问题。讨论非定常运动的两类典型非线性发展方程(双曲型守恒系统和耗散系统)数值格式的计算稳定性，给出一种判定差分格式计算稳定性的新方法。数值试验证明该方法是实用的和有效的，得到的判据的确是保证差分格式计算稳定的必要条件；指出非线性计算不稳定与原始微分方程解的性质密切有关，同时还和具体格式结构及初值形式有关。
비선성계산은정성시계산수학、계산물리、계산기상등학과중적일개중요문제。토론비정상운동적량류전형비선성발전방정(쌍곡형수항계통화모산계통)수치격식적계산은정성，급출일충판정차분격식계산은정성적신방법。수치시험증명해방법시실용적화유효적，득도적판거적학시보증차분격식계산은정적필요조건；지출비선성계산불은정여원시미분방정해적성질밀절유관，동시환화구체격식결구급초치형식유관。
The stability of nonlinear computation is important in numerical mathematics, computing physics and numerical weather forecasting. Taken two kinds of evolution equations as classical models (The hyperbolicconservation system and dissipation system), a new method for evaluating the computational stability is proposed. It is proved to be practical and effective by several numerical examples. The stability criteria obtained by this method are the necessary conditions of computational stability. It is emphasized the strong dependence of nonlinear computational stability on the properties of original differential equation solution. It depends on structure of the schemes.and the initial condition too.