The validity and accuracy of our new numerical approach implemented in KISSA-1D software when applied to a theoretical study of different types of electrochemiluminescence (ECL) is established by comparison with existing analytical solutions and others specifically derived in this work, as well as with independent numerical solutions obtained by using commercial software. The efficiency and comprehensiveness of this approach are illustrated by using a representative series of published ECL reaction schemes taken as typical case studies when ECL is generated by a single electrode under amperometric or voltammetric conditions, even when rate constants used in the simulations far exceed any of their realistic experimental limits.