On the method of modified equations. IV: Numerical techniques based on the modified equation for the Euler forward difference method
The paper is the fourth of a series dealing with the assessment of modified equation methods as a means for the analysis of existing finite difference schemes and for the development of new numerical ones. [For parts III and V see ibid. 103, No.~2-3, 179-212 and 241-285 (1999; reviewed above and below).] The validity of the modified equation based on the third equivalent method (described in the first paper (reviewed above)) is studied as a method for the development on new numerical techniques. Direct-correction techniques are used for the estimation and correction of the truncation error terms in the modified equation. The resulting numerical methods are explicit and their absolute stability is better than that of the original Euler method. The asymptotic successive-correction techniques are applied to the correction of the modified equations. The direct-correction and successive-correction numerical techniques are applied to some systems of ordinary differential equations and are compared with Runge-Kutta techniques.
asymptotic successive-correction techniques
scientific article; zbMATH DE number 1311047