A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear advection-diffusion processes represented by (2+1)-dimensional Burgers equation. The IELDTM is adaptively constructed as stability preserved and high order time integrator for spatially discretized Burgers equation. For spatial discretization of the model equation, the Chebyshev spectral collocation method (ChCM) is utilized. A robust stability analysis and global error analysis of the IELDTM are presented with respect to the direction parameter \theta. With the help of the global error analysis, adaptivity equations are derived to minimize the computational costs of the algorithms. The produced method is shown to eliminate the accuracy disadvantage of the classical \theta-method and the stability disadvantages of the existing DTM-based methods. Two examples of the Burgers equation in one and two dimensions have been solved via the ChCM-IELDTM hybridization, and the produced results are compared with the literature. The present time integrator has been proven to produce more accurate numerical results than the MATLAB solvers, ode45 and ode15s.
翻译:此处为以(2+1)-维汉堡方程式为代表的非线性对冲反扩散过程的时间整合而产生一种新的隐含局部差分变法(IELDTM),IELDTM是作为空间离散汉堡方程式的稳定性保存和高顺序时间整合器而适应性构造的。对于模型方程式的空间离散,使用了Chebyshev光谱合位法(ChCM),结合了方向参数\theta,对IELDTM进行了稳健的稳定性分析和全球错误分析。在全球错误分析的帮助下,得出适应性方程式,以尽量减少算法的计算成本。所产生的方法显示消除经典\theta-method的准确性劣势以及现有DTM方法的稳定性劣势。一个和两个维度的Burgers方程式的两个实例已经通过CM-IELDTM的混合化得到解决,所产生的结果与文献进行了比较。当前绘图器中的时间已被证明比MATLAMode15和Mode的解算器更精确的数字结果。