更改

Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables. For example, the position of a rigid body is specified by six parameters, but the configuration of a fluid is given by the continuous distribution of several parameters, such as the temperature, pressure, and so forth. The dynamics for the rigid body take place in a finite-dimensional configuration space; the dynamics for the fluid occur in an infinite-dimensional configuration space. This distinction usually makes PDEs much harder to solve than ordinary differential equations (ODEs), but here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include acoustics, fluid dynamics, electrodynamics, and heat transfer.

Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables. For example, the position of a rigid body is specified by six parameters, but the configuration of a fluid is given by the continuous distribution of several parameters, such as the temperature, pressure, and so forth. The dynamics for the rigid body take place in a finite-dimensional configuration space; the dynamics for the fluid occur in an infinite-dimensional configuration space. This distinction usually makes PDEs much harder to solve than ordinary differential equations (ODEs), but here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include acoustics, fluid dynamics, electrodynamics, and heat transfer.

偏微分方程(简称为PDEs)涉及到连续变量的变化率。例如，刚体的位置是由六个参数确定的，而流体的形状是由几个参数的连续分布给出的，如温度、压力等。刚体的动力学过程发生在有限维位形空间中，流体的动力学过程发生在无限维位形空间中。这种区别通常使偏微分方程比常微分方程更难求解，但是线性问题也有简单的解。使用偏微分方程的经典领域包括声学、流体力学、电动力学和传热学。

偏微分方程(简称为PDEs)涉及到方程相对于连续变量的变化率。例如，刚体的位置是由六个参数确定的，而流体的状态是由几个参数的连续分布给出的，如温度、压力等。刚体的动力学过程发生在有限维状态空间中，流体的动力学过程发生在无限维状态空间中。这种区别通常使偏微分方程比常微分方程更难求解，但是线性问题仍然有简单的求解方式。使用偏微分方程的经典领域包括声学、流体力学、电动力学和传热学。