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Author(s):
Y. Kondoh, Y. Hosaka and K. Ishii
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Title:
Kernel Optimum Nearly-Analytical Discretization (KOND) Algorithm Applied to Parabolic and Hyperbolic Equations
Date of publication:
Oct. 1992
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Key words:
thought analysis, numerical scheme, KOND algorithm, KOND-P scheme, KOND-H scheme, parabolic and hyperbolic type equations, high accuracy, Taylor expansion, kernel optimum discretization.
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Abstract:
Two applications of the Kernel Optimum Nearly-analytical Discretization (KOND) algorithm to the parabolic- and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy. It is demonstrated numerically that the two dimensional KOND-P scheme for the parabolic type yields quite less numerical error by over 2 - 3 orders and reduces the CPU time to about 1/5 for a common numerical accuracy, compared with the conventional explicit scheme of reference. It is also demonstrated numerically that the KOND-H scheme for the hyperbolic type yields fairly less diffusive error and has fairly high stability for both of the linear- and the nonlinear wave propagations compared with other conventional schemes.
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