Notwithstanding any other provision of law, in the case of a deficiency in the payment of taxes due and payable pursuant to this chapter, the tax collector, with the approval of the board of supervisors, may accept such partial payment from the taxpayer. Such partial payments are to be applied first to all penalties, interest and costs with the balance being applied to the taxes due. The difference between the amount paid by the taxpayer and the amount due shall be treated as a delinquent tax in the same manner as any other delinquent tax.