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SEMI-EXPLICIT MULTISTEP ADAMS-BASHFORTH-MOULTON METHODS FOR SOLVING STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

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The computational efficiency of semi-explicit and semi-implicit multistep methods of numerical integration when applied to simulation of seven-dimensional stiff system of ordinary differential equations is studied. A general description of semi-explicit and semi-implicit Adams-Bashforth-Moulton methods is presented. Performance of solvers based on investigated methods of the fourth order is compared to that of solvers using Adams methods and the backward differentiation formula. The computational experiments carried out confirm that the proposed modifications of the Adams-Bashforth-Moulton method demonstarate the best performance among the considered multistep schemes, when simulating with a constant and variable integration step. It is assumed that the obtained results can be used to speed up numerical modeling in modeling subsystems of computer-aided design systems.

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