本文提出了求解二维变系数G方程的高精度交替方向隐式(ADI)格式,该方法在物理、金融和计算数学中具有重要应用。我们分析了该格式的稳定性,并进行了数值实验,比较了不同格式的绝对误差,验证了ADI格式的有效性。In this paper, we propos...本文提出了求解二维变系数G方程的高精度交替方向隐式(ADI)格式,该方法在物理、金融和计算数学中具有重要应用。我们分析了该格式的稳定性,并进行了数值实验,比较了不同格式的绝对误差,验证了ADI格式的有效性。In this paper, we propose high-accuracy Alternating Direction Implicit (ADI) scheme for solving two-dimensional variable coefficient G-equations, which have significant applications in physics, finance and computational mathematics. The stability of the scheme is analyzed, and numerical experiment is conducted to compare absolute errors across different schemes, confirming the effectiveness of the scheme.展开更多
本文主要研究了一类含应力项的非线性变系数波动方程在不同能级下解的整体存在性及其爆破行为。基于泛函估计方法,构建了位势井框架,并在此基础上给出了次临界能级下解全局存在的条件及其解的爆破时间估计。同时,还探讨了临界能级下全...本文主要研究了一类含应力项的非线性变系数波动方程在不同能级下解的整体存在性及其爆破行为。基于泛函估计方法,构建了位势井框架,并在此基础上给出了次临界能级下解全局存在的条件及其解的爆破时间估计。同时,还探讨了临界能级下全局解存在的条件。This paper mainly studies the existence of global solutions and the blow-up behavior for a class of nonlinear variable coefficient wave equations with stress term under different energy levels. Based on functional estimates, the potential well framework is constructed, and the conditions for the existence of global solutions and blow-up time under subcritical energy levels are provided. Additionally, the conditions for the existence of global solutions at the critical energy level are discussed.展开更多
文摘本文提出了求解二维变系数G方程的高精度交替方向隐式(ADI)格式,该方法在物理、金融和计算数学中具有重要应用。我们分析了该格式的稳定性,并进行了数值实验,比较了不同格式的绝对误差,验证了ADI格式的有效性。In this paper, we propose high-accuracy Alternating Direction Implicit (ADI) scheme for solving two-dimensional variable coefficient G-equations, which have significant applications in physics, finance and computational mathematics. The stability of the scheme is analyzed, and numerical experiment is conducted to compare absolute errors across different schemes, confirming the effectiveness of the scheme.
文摘本文主要研究了一类含应力项的非线性变系数波动方程在不同能级下解的整体存在性及其爆破行为。基于泛函估计方法,构建了位势井框架,并在此基础上给出了次临界能级下解全局存在的条件及其解的爆破时间估计。同时,还探讨了临界能级下全局解存在的条件。This paper mainly studies the existence of global solutions and the blow-up behavior for a class of nonlinear variable coefficient wave equations with stress term under different energy levels. Based on functional estimates, the potential well framework is constructed, and the conditions for the existence of global solutions and blow-up time under subcritical energy levels are provided. Additionally, the conditions for the existence of global solutions at the critical energy level are discussed.
