We propose a new method for solving Initial Value Problems (IVPs). Our method is based on analog computing and has the potential to almost eliminate traditional switching time in digital computing. The approach can be used to simulate large systems longer, faster, and with higher accuracy. Many algorithms for Model-Based Diagnosis use numerical integration to simulate physical systems. The numerical integration process is often either computationally expensive or imprecise. We propose a new method, based on Field-Programmable Analog Arrays (FPAAs) that has the potential to overcome many practical problems. We envision a software/hardware framework for solving systems of simultaneous Ordinary Differential Equations (ODEs) in fraction of the time of traditional numerical algorithms. In this paper we describe the solving of an IVP with the help of an Analog Computing Unit (ACU). To do this we build a special calculus based on operational amplifiers (op-amps) with local feedback. We discuss the implementation of the ACU on an Integrated Circuit (IC). We analyze the working if the IC and simulate the dynamic Lotka-Volterra system with the de-facto standard tool for electrical simulation: Spice.