A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions
نویسندگان
چکیده
منابع مشابه
A direct Numerov sixth order numerical scheme to accurately solve the unidimensional Poisson equation with Dirichlet boundary conditions
In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.
متن کاملA Posteriori Error Estimation for the Poisson Equation with Mixed Dirichlet/Neumann Boundary Conditions
The present work is devoted to the a posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Using the duality technique we derive a reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H, indepe...
متن کاملA sixth-order compact finite difference scheme to the numerical solutions of Burgers' equation
Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...
متن کاملA numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method
In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...
متن کاملA conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains
In this paper we present a conservative numerical method for the Cahn–Hilliard equation with Dirichlet boundary conditions in complex domains. The method uses an unconditionally gradient stable nonlinear splitting numerical scheme to remove the highorder time-step stability constraints. The continuous problemhas the conservation ofmass and we prove the conservative property of the proposed disc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Superconductivity and Novel Magnetism
سال: 2009
ISSN: 1557-1939,1557-1947
DOI: 10.1007/s10948-009-0544-z