动力学偏微分方程的卷积型DQ半解析法

A Convolution Type DQ Semi-analytic Approach for Dynamics Differential Equations

文章通过卷积方法将数学物理方程中典型的动力学方程构造成包含初始条件的新的具有完整初值问题特征的动力学控制方程。对新的控制方程在时间域取解析函数,在空间域采用离散的DQ法。这种方法具有与卷积型Gurtin原理完全等效的效果,又避免了Gurtin泛函的复杂性,还避免了误差积累和解的稳定性等问题。经实际计算表明,该方法是一种精度好效率高的求解动力学偏微分方程问题计算方法。

In the paper, dynamics differential equations in mathematical physics are deduced by the method of convolution calculation equations blended With initial conditions are obtained, whose solutions are then sought through the use of differential quadrature approximation in space domain, so was in time domain. This approach obtains the same effects with Gurtin variation principles, at the same time,it avoids the complexity of gurtin functional. The results of the examples show that the method has excellent accuracy and efficiency for the resolution of dynamic differential equations in mathematical physics.