کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
567225 | 1452137 | 2015 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Implementation and solution of the diffusion–reaction equation using high-order methods Implementation and solution of the diffusion–reaction equation using high-order methods](/preview/png/567225.png)
The orthogonal collocation, Galerkin, tau and least-squares methods are applied to solve a diffusion–reaction problem. In general, the least-squares method suffers from lower accuracy than the other weighted residual methods. The least-squares method holds the most complex linear algebra theory and is thus associated with the most complex implementation. On the other hand, an advantage of the least-squares method is that it always produces a symmetric and positive definite system matrix which can be solved with an efficient iterative technique such as the conjugate gradient method or its preconditioned version. For the present problem, neither the Galerkin, tau and orthogonal collocation techniques produce symmetric and positive definite system matrices, hence the conjugate gradient method is not applicable for these numerical techniques.
Journal: Advances in Engineering Software - Volume 80, February 2015, Pages 33–46