Modified Extended BDF Time-Integration Methods, Applied to Circuit Equations
Electric circuits designers are frequently interested in the transient behaviour of the designed circuit. A common method for time integration of the Differential Algebraic circuit Equations (DAE) is the Backward Differentiation Formula (BDF) method. In 1983, J. Cash proposed the Modified Extended BDF (MEBDF) method, which combines better stability properties and higher order of convergence than BDF, but requires more computations per step. We prove reduction of convergence order for MEBDF when applied to DAE’s with higher DAE-index. However, because in practice, in circuit analysis, the DAE-index does not exceed 2, the reduction is quite moderate and it equals the BDF-order in that case. One gains better, or even unconditional, stability. One also obtains consistent solutions.
KeywordsConsistent Solution Inverse Function Theorem Initial Valu Backward Differentiation Formula Algebraic Part
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