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Kernel Optimum Nearly-analytical Discretization (KOND) algorithm. Applied to parabolic and hyperbolic equations

机译：核优化近分析离散化（KOND）算法。适用于抛物线和双曲方程

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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. (author). (ERA citation 18:014155)

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