The present invention relates to an improved method for computer-aided electrical circuit simulation which combines circuit partitioning, modified nodal formulation and conjugate-gradient solution method to efficiently analyze large electrical circuit networks. Circuit partitioning is used to create sub-circuits which isolate the passive elements of the electrical circuit. Modified nodal formulation is used to formulate matrices representative of the resultant sub-circuits. All matrices resulting from the sub-circuits containing only passive elements will be positive-definite symmetric and are efficiently solved using conjugate gradient method. Conjugate-gradient method is known to be an extremely efficient method for solving matrices of this type.