Journal of Difference Equations and Applications ( IF 1.1 ) Pub Date : 2021-05-03 , DOI: 10.1080/10236198.2021.1920936 Geetan Manchanda 1 , R. K. Mohanty 2 , Arshad Khan 1
This paper describes a novel implicit method of order 2 in y- and 3 in x-direction in exponential form, by exploiting off-step discretization to solve numerically non-linear elliptic partial differential equations in a rectangular region. We use variable mesh in x-direction and constant mesh in y-direction in order to solve convection–diffusion equation for large values of the coefficient of convection term. This method uses 9-point compact stencil. Detailed derivation and convergence procedure of the proposed method have been discussed. The method has been generalized to solve non-linear elliptic equations in vector form. The method is validated on several benchmark problems showing that formulation produces satisfactory results.
中文翻译:
非线性椭圆边值问题求解的指数形式的高精度紧凑半常数网格离步离散化
本文描述了一种新的隐式隐式方法,即y方向2 阶和x方向3阶指数形式,通过利用离步离散化进行数值求解矩形区域中的非线性椭圆偏微分方程。我们在x方向使用可变网格,在y方向使用恒定网格,以便求解对流项系数较大的对流扩散方程。此方法使用 9 点紧凑型模板。已经讨论了所提出方法的详细推导和收敛过程。该方法已推广到求解向量形式的非线性椭圆方程。该方法在几个基准问题上得到验证,表明配方产生了令人满意的结果。