PCA: Simulating erroneous equations for error-visualization

Abstract

This paper presents the method of simulating the simultaneous equations which are over/under-constrained by the learner's misconception (partial constraint analysis: PCA). It can deal with arbitrary linear differential and/or algebraic equations with erroneous parts which preserve linearity. The procedure is as follows: (1) to generate the network which describes the constraints among the variables in equations (causal relation network: cn); (2) to abstract the subgraphs in which variables can be calculated (executed) independently of the rest (partial causal chains: pc); (3) to enumerate the combinations of pces which can be executed simultaneously; and (4) to execute the selected combination by supplying the driving data exogenously for simulating the behavior of the erroneous system. An example of application to a simple electric circuit is also presented.