Galerkin spectral method for the vorticity and stream function equations
Journal of Computational Physics
Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
Application of Taylor series in obtaining the orthogonal operational matrix
Computers & Mathematics with Applications
A tau approach for solution of the space fractional diffusion equation
Computers & Mathematics with Applications
A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations
Mathematical and Computer Modelling: An International Journal
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 0.09 |
In this paper, a Legendre-Galerkin method for solving second-order elliptic differential equations subject to the most general nonhomogeneous Robin boundary conditions is presented. The homogeneous Robin boundary conditions are satisfied exactly by expanding the unknown variable using a polynomial basis of functions which are built upon the Legendre polynomials. The direct solution algorithm here developed for the homogeneous Robin problem in two-dimensions relies upon a tensor product process. Nonhomogeneous Robin data are taken into account by means of a lifting. Such a lifting is performed in two successive steps, the first one to account for the data specified at the corners and the second one to account for the boundary values prescribed in the interior of the sides. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented.