Integral equations describing controlled-potential transient experiments at planar interfaces, and under conditions of diffusion in one-dimensional finite space, occur in various areas of electrochemistry. Former simulation methods used to solve such equations were rather crudely approximate and non-automatic. In the present work computationally inexpensive approximations to the integral transformation kernels occurring in these equations are determined, that possess the best accuracy achievable within the standard floating point arithmetic. The approximations are combined with the recently developed adaptive Huber method for solving electrochemical integral equations of the Volterra type. The resulting algorithm is tested on representative examples of transient experiments: potential step chronoamperometry for irreversible electron transfer, and cyclic voltammetry for irreversible and reversible electron transfers. The performance of the method is found similar to that previously reported for integral equations involving kernels specific for semi-infinite diffusion. Desired accuracy of the solutions is achieved automatically, depending on user-selected values of the error tolerance parameter. Errors corresponding to the range from about 10(-2) of the maximum solution value, down to about 10(-7) or even smaller, can be easily achieved at a modest computational cost. (C) 2012 Elsevier B.V. All rights reserved.