Implementation of generalized finite difference formulas and truncation errors for each derivative

Journal Article · · International Communications in Heat and Mass Transfer; (United States)

DOI:https://doi.org/10.1016/0735-1933(94)90004-3· OSTI ID:7018916

Kou, H S; Lee, C L ^[1]

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1. Tatung Inst. of Tech., Taipei (Taiwan, Province of China). Dept. of Mechanical Engineering

Through Taylor series expansion, a generalized formulation which can show any finite difference expression along with its truncation error for each derivative has been introduced in the present study. Thereafter, several well-known finite difference and finite element formulas for the first and second derivatives are demonstrated to compare with their truncation errors. As to the applications, higher-order terms of truncation error can be incorporated into finite difference equation to get more accurate results. In addition, a new scheme is proposed to generate an optimum finite difference equation where its total truncation error is minimized.

• OSTI ID: 7018916
• Journal Information: International Communications in Heat and Mass Transfer; (United States), Vol. 21:3; ISSN 0735-1933
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
FINITE DIFFERENCE METHOD
DATA COVARIANCES
MATHEMATICS
RELIABILITY
RESOLUTION
CALCULATION METHODS
ITERATIVE METHODS
NUMERICAL SOLUTION
420400* - Engineering- Heat Transfer & Fluid Flow
990200 - Mathematics & Computers