The improved linear multistep methods for differential equations with piecewise continuous arguments |
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Authors: | MH Song X Liu |
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Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
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Abstract: | This paper deals with the convergence of the linear multistep methods for the equation x′(t) = ax(t) + a0x(t]). Numerical experiments demonstrate that the 2-step Adams-Bashforth method is only of order p = 0 when applied to the given equation. An improved linear multistep methods is constructed. It is proved that these methods preserve their original convergence order for ordinary differential equations (ODEs) and some numerical experiments are given. |
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Keywords: | Piecewise continuous arguments Improved linear multistep methods Convergence Numerical solution Delay differential equation |
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