ISSN:
0271-2091
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
In this paper a new, highly accurate method called PH is presented for the numerical integration of partial differential equations. The method is applied for the solution of the one-dimensional diffusion equation. Upon integrating the equation within a subdomain of space and time using the prismoidal approximation, a three-point implicit scheme is obtained with a truncation error of order O(k4, h6), where k and h represent the time and space steps respectively. The method is stable under the condition s = αk/h2 ≤ S(δ), where the function S(δ) increases as the parameter δ decreases from 1/12 to negative values. In practice the method behaves as unconditionally stable upon choosing an appropriate value for δ. A new formula is also adopted for the implementation of a Neumann boundary condition, introducing a truncation error of order O(h4). Numerical solutions are obtained incorporating Dirichlet and Neumann boundary conditions. The results prove that our method is far more accurate than any other-implicit or explicit method.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650180303
