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The therm istor problem is an initial-boundary value problem ofcoupled nonlineardif- ferentialequations.The nonlinear PDEs consist of a heat equation w ith the Joule heating as a source and a currentconservation equation w ith tem perature-dependentelectricalconductivity. This problem has im portant applications in industry.In this paper,A new finite difference schem e is proposed on nonuniform rectangularpartition forthe therm istor problem .In thetheo- reticalanalyses,the second-order error estim ates are obtained for electricalpotentialin discrete L2 and H1 norm s,and for the tem perature in L2 norm .In order to getthese second-order error estim ates,the Joule heating source is used in a changed equivalentform .
The therm istor problem is an initial-boundary value problem of coupled nonlineard-ferentialequations.The nonlinear PDEs consist of a heat equation w ith the Joule heating as a source and a currentconservation equation w ith tem perature-dependentelectricalconductivity. This problem has im portant applications in In the paper, A new finite difference schem e is proposed on nonuniform rectangular partition forthe thermistor problem. In the theo-reticalanalyses, the second-order error estim ates are obtained for electrical potential difference discrete L2 and H1 norm s, and for the tem perature in L2 norm .In order to getthese second-order error estim ates, the Joule heating source is used in a changed equivalentform.